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Index Entry  Section

$
$, shell prompt: Conventions used in this manual

2
2D histograms: Two dimensional histograms
2D random direction vector: Spherical Vector Distributions

3
3-j symbols: Coupling Coefficients
3D random direction vector: Spherical Vector Distributions

6
6-j symbols: Coupling Coefficients

9
9-j symbols: Coupling Coefficients

A
acceleration of series: Series Acceleration
acosh: Elementary Functions
Adams method: Stepping Functions
Adaptive step-size control, differential equations: Adaptive Step-size Control
Ai(x): Airy Functions and Derivatives
Airy functions: Airy Functions and Derivatives
Akima splines: Interpolation Types
aliasing of arrays: Aliasing of arrays
alternative optimized functions: Alternative optimized functions
AMAX, Level-1 BLAS: Level 1 GSL BLAS Interface
Angular Mathieu Functions: Angular Mathieu Functions
angular reduction: Restriction Functions
ANSI C, use of: Using the library
Apell symbol, see Pochhammer symbol: Pochhammer Symbol
approximate comparison of floating point numbers: Approximate Comparison of Floating Point Numbers
arctangent integral: Arctangent Integral
argument of complex number: Properties of complex numbers
arithmetic exceptions: Setting up your IEEE environment
asinh: Elementary Functions
astronomical constants: Astronomy and Astrophysics
ASUM, Level-1 BLAS: Level 1 GSL BLAS Interface
atanh: Elementary Functions
atomic physics, constants: Atomic and Nuclear Physics
autoconf, using with GSL: Autoconf Macros
AXPY, Level-1 BLAS: Level 1 GSL BLAS Interface

B
B-spline wavelets: DWT Initialization
Bader and Deuflhard, Bulirsch-Stoer method.: Stepping Functions
balancing matrices: Balancing
Basic Linear Algebra Subroutines (BLAS): BLAS Support
Basic Linear Algebra Subroutines (BLAS): GSL CBLAS Library
basis splines, B-splines: Basis Splines
basis splines, derivatives: Evaluation of B-spline basis function derivatives
basis splines, evaluation: Evaluation of B-spline basis functions
basis splines, examples: Example programs for B-splines
basis splines, Greville abscissae: Working with the Greville abscissae
basis splines, initializing: Initializing the B-splines solver
basis splines, Marsden-Schoenberg points: Working with the Greville abscissae
basis splines, overview: Overview of B-splines
BDF method: Stepping Functions
Bernoulli trial, random variates: The Bernoulli Distribution
Bessel functions: Bessel Functions
Bessel Functions, Fractional Order: Regular Bessel Function - Fractional Order
best-fit parameters, covariance: Computing the covariance matrix of best fit parameters
Beta distribution: The Beta Distribution
Beta function: Beta Functions
Beta function, incomplete normalized: Incomplete Beta Function
BFGS algorithm, minimization: Multimin Algorithms with Derivatives
Bi(x): Airy Functions and Derivatives
bias, IEEE format: Representation of floating point numbers
bidiagonalization of real matrices: Bidiagonalization
binning data: Histograms
Binomial random variates: The Binomial Distribution
biorthogonal wavelets: DWT Initialization
bisection algorithm for finding roots: Root Bracketing Algorithms
Bivariate Gaussian distribution: The Bivariate Gaussian Distribution
BLAS: BLAS Support
BLAS, Low-level C interface: GSL CBLAS Library
blocks: Vectors and Matrices
bounds checking, extension to GCC: Accessing vector elements
breakpoints: Using gdb
Brent’s method for finding minima: Minimization Algorithms
Brent’s method for finding roots: Root Bracketing Algorithms
Broyden algorithm for multidimensional roots: Algorithms without Derivatives
BSD random number generator: Unix random number generators
bug-gsl mailing list: Reporting Bugs
bugs, how to report: Reporting Bugs
Bulirsch-Stoer method: Stepping Functions

C
C extensions, compatible use of: Using the library
C++, compatibility: Compatibility with C++
C99, inline keyword: Inline functions
Carlson forms of Elliptic integrals: Definition of Carlson Forms
Cash-Karp, Runge-Kutta method: Stepping Functions
Cauchy distribution: The Cauchy Distribution
Cauchy principal value, by numerical quadrature: QAWC adaptive integration for Cauchy principal values
CBLAS: BLAS Support
CBLAS, Low-level interface: GSL CBLAS Library
CDFs, cumulative distribution functions: Random Number Distributions
ce(q,x), Mathieu function: Angular Mathieu Functions
Chebyshev series: Chebyshev Approximations
checking combination for validity: Combination properties
checking multiset for validity: Multiset properties
checking permutation for validity: Permutation properties
Chi(x): Hyperbolic Integrals
Chi-squared distribution: The Chi-squared Distribution
Cholesky decomposition: Cholesky Decomposition
Ci(x): Trigonometric Integrals
Clausen functions: Clausen Functions
Clenshaw-Curtis quadrature: Integrands with weight functions
CMRG, combined multiple recursive random number generator: Random number generator algorithms
code reuse in applications: Code Reuse
combinations: Combinations
combinatorial factor C(m,n): Factorials
combinatorial optimization: Simulated Annealing
comparison functions, definition: Sorting objects
compatibility: Using the library
compiling programs, include paths: Compiling and Linking
compiling programs, library paths: Linking programs with the library
complementary incomplete Gamma function: Incomplete Gamma Functions
complete Fermi-Dirac integrals: Complete Fermi-Dirac Integrals
complex arithmetic: Complex arithmetic operators
complex cosine function, special functions: Trigonometric Functions for Complex Arguments
Complex Gamma function: Gamma Functions
complex hermitian matrix, eigensystem: Complex Hermitian Matrices
complex log sine function, special functions: Trigonometric Functions for Complex Arguments
complex numbers: Complex Numbers
complex sinc function, special functions: Circular Trigonometric Functions
complex sine function, special functions: Trigonometric Functions for Complex Arguments
confluent hypergeometric function: Laguerre Functions
confluent hypergeometric functions: Hypergeometric Functions
conical functions: Legendre Functions and Spherical Harmonics
Conjugate gradient algorithm, minimization: Multimin Algorithms with Derivatives
conjugate of complex number: Complex arithmetic operators
constant matrix: Initializing matrix elements
constants, fundamental: Fundamental Constants
constants, mathematical—defined as macros: Mathematical Constants
constants, physical: Physical Constants
constants, prefixes: Prefixes
contacting the GSL developers: Further Information
conventions, used in manual: Conventions used in this manual
convergence, accelerating a series: Series Acceleration
conversion of units: Physical Constants
cooling schedule: Simulated Annealing algorithm
COPY, Level-1 BLAS: Level 1 GSL BLAS Interface
correlation, of two datasets: Correlation
cosine function, special functions: Circular Trigonometric Functions
cosine of complex number: Complex Trigonometric Functions
cost function: Simulated Annealing
Coulomb wave functions: Coulomb Functions
coupling coefficients: Coupling Coefficients
covariance matrix, from linear regression: Linear regression
covariance matrix, linear fits: Fitting Overview
covariance matrix, nonlinear fits: Computing the covariance matrix of best fit parameters
covariance, of two datasets: Covariance
cquad, doubly-adaptive integration: CQUAD doubly-adaptive integration
CRAY random number generator, RANF: Other random number generators
cubic equation, solving: Cubic Equations
cubic splines: Interpolation Types
cumulative distribution functions (CDFs): Random Number Distributions
Cylindrical Bessel Functions: Regular Cylindrical Bessel Functions

D
Daubechies wavelets: DWT Initialization
Dawson function: Dawson Function
DAXPY, Level-1 BLAS: Level 1 GSL BLAS Interface
debugging numerical programs: Using gdb
Debye functions: Debye Functions
denormalized form, IEEE format: Representation of floating point numbers
deprecated functions: Deprecated Functions
derivatives, calculating numerically: Numerical Differentiation
determinant of a matrix, by LU decomposition: LU Decomposition
Deuflhard and Bader, Bulirsch-Stoer method.: Stepping Functions
DFTs, see FFT: Fast Fourier Transforms
diagonal, of a matrix: Creating row and column views
differential equations, initial value problems: Ordinary Differential Equations
differentiation of functions, numeric: Numerical Differentiation
digamma function: Psi (Digamma) Function
dilogarithm: Dilogarithm
direction vector, random 2D: Spherical Vector Distributions
direction vector, random 3D: Spherical Vector Distributions
direction vector, random N-dimensional: Spherical Vector Distributions
Dirichlet distribution: The Dirichlet Distribution
discontinuities, in ODE systems: Evolution
Discrete Fourier Transforms, see FFT: Fast Fourier Transforms
discrete Hankel transforms: Discrete Hankel Transforms
Discrete Newton algorithm for multidimensional roots: Algorithms without Derivatives
Discrete random numbers: General Discrete Distributions
Discrete random numbers: General Discrete Distributions
Discrete random numbers: General Discrete Distributions
Discrete random numbers: General Discrete Distributions
Discrete random numbers, preprocessing: General Discrete Distributions
divided differences, polynomials: Divided Difference Representation of Polynomials
division by zero, IEEE exceptions: Setting up your IEEE environment
dollar sign $, shell prompt: Conventions used in this manual
DOT, Level-1 BLAS: Level 1 GSL BLAS Interface
double factorial: Factorials
double precision, IEEE format: Representation of floating point numbers
downloading GSL: Obtaining GSL
DWT initialization: DWT Initialization
DWT, mathematical definition: DWT Definitions
DWT, one dimensional: DWT in one dimension
DWT, see wavelet transforms: Wavelet Transforms
DWT, two dimensional: DWT in two dimension

E
e, defined as a macro: Mathematical Constants
E1(x), E2(x), Ei(x): Exponential Integral
eigenvalues and eigenvectors: Eigensystems
elementary functions: Mathematical Functions
elementary operations: Elementary Operations
elliptic functions (Jacobi): Elliptic Functions (Jacobi)
elliptic integrals: Elliptic Integrals
energy function: Simulated Annealing
energy, units of: Thermal Energy and Power
erf(x): Error Functions
erfc(x): Error Functions
Erlang distribution: The Gamma Distribution
error codes: Error Codes
error codes, reserved: Error Codes
error function: Error Functions
Error handlers: Error Handlers
error handling: Error Handling
error handling macros: Using GSL error reporting in your own functions
Errors: Error Handling
estimated standard deviation: Statistics
estimated variance: Statistics
Eta Function: Eta Function
euclidean distance function, hypot: Elementary Functions
euclidean distance function, hypot: Elementary Functions
Euler’s constant, defined as a macro: Mathematical Constants
evaluation of polynomials: Polynomial Evaluation
evaluation of polynomials, in divided difference form: Divided Difference Representation of Polynomials
examples, conventions used in: Conventions used in this manual
exceptions, C++: Compatibility with C++
exceptions, floating point: Handling floating point exceptions
exceptions, IEEE arithmetic: Setting up your IEEE environment
exchanging permutation elements: Accessing permutation elements
exp: Exponential Functions
expm1: Elementary Functions
exponent, IEEE format: Representation of floating point numbers
Exponential distribution: The Exponential Distribution
exponential function: Exponential Functions
exponential integrals: Exponential Integrals
Exponential power distribution: The Exponential Power Distribution
exponential, difference from 1 computed accurately: Elementary Functions
exponentiation of complex number: Elementary Complex Functions
extern inline: Inline functions

F
F-distribution: The F-distribution
factorial: Factorials
factorial: Factorials
factorization of matrices: Linear Algebra
false position algorithm for finding roots: Root Bracketing Algorithms
Fast Fourier Transforms, see FFT: Fast Fourier Transforms
Fehlberg method, differential equations: Stepping Functions
Fermi-Dirac function: Fermi-Dirac Function
FFT: Fast Fourier Transforms
FFT mathematical definition: Mathematical Definitions
FFT of complex data, mixed-radix algorithm: Mixed-radix FFT routines for complex data
FFT of complex data, radix-2 algorithm: Radix-2 FFT routines for complex data
FFT of real data: Overview of real data FFTs
FFT of real data, mixed-radix algorithm: Mixed-radix FFT routines for real data
FFT of real data, radix-2 algorithm: Radix-2 FFT routines for real data
FFT, complex data: Overview of complex data FFTs
finding minima: One dimensional Minimization
finding roots: One dimensional Root-Finding
finding zeros: One dimensional Root-Finding
fits, multi-parameter linear: Multi-parameter fitting
fitting: Least-Squares Fitting
fitting, using Chebyshev polynomials: Chebyshev Approximations
Fj(x), Fermi-Dirac integral: Complete Fermi-Dirac Integrals
Fj(x,b), incomplete Fermi-Dirac integral: Incomplete Fermi-Dirac Integrals
flat distribution: The Flat (Uniform) Distribution
Fletcher-Reeves conjugate gradient algorithm, minimization: Multimin Algorithms with Derivatives
floating point exceptions: Handling floating point exceptions
floating point numbers, approximate comparison: Approximate Comparison of Floating Point Numbers
floating point registers: Examining floating point registers
force and energy, units of: Force and Energy
Fortran range checking, equivalent in gcc: Accessing vector elements
Four-tap Generalized Feedback Shift Register: Random number generator algorithms
Fourier integrals, numerical: QAWF adaptive integration for Fourier integrals
Fourier Transforms, see FFT: Fast Fourier Transforms
Fractional Order Bessel Functions: Regular Bessel Function - Fractional Order
free software, explanation of: GSL is Free Software
frexp: Elementary Functions
functions, numerical differentiation: Numerical Differentiation
fundamental constants: Fundamental Constants

G
Gamma distribution: The Gamma Distribution
gamma functions: Gamma Functions
Gauss-Kronrod quadrature: Integrands without weight functions
Gaussian distribution: The Gaussian Distribution
Gaussian distribution, bivariate: The Bivariate Gaussian Distribution
Gaussian Tail distribution: The Gaussian Tail Distribution
gcc extensions, range-checking: Accessing vector elements
gcc warning options: GCC warning options for numerical programs
gdb: Using gdb
Gegenbauer functions: Gegenbauer Functions
GEMM, Level-3 BLAS: Level 3 GSL BLAS Interface
GEMV, Level-2 BLAS: Level 2 GSL BLAS Interface
general polynomial equations, solving: General Polynomial Equations
generalized eigensystems: Real Generalized Nonsymmetric Eigensystems
generalized hermitian definite eigensystems: Complex Generalized Hermitian-Definite Eigensystems
generalized symmetric eigensystems: Real Generalized Symmetric-Definite Eigensystems
Geometric random variates: The Geometric Distribution
Geometric random variates: The Hypergeometric Distribution
GER, Level-2 BLAS: Level 2 GSL BLAS Interface
GERC, Level-2 BLAS: Level 2 GSL BLAS Interface
GERU, Level-2 BLAS: Level 2 GSL BLAS Interface
Givens Rotation, BLAS: Level 1 GSL BLAS Interface
Givens Rotation, Modified, BLAS: Level 1 GSL BLAS Interface
GNU General Public License: Introduction
golden section algorithm for finding minima: Minimization Algorithms
GSL_C99_INLINE: Inline functions
GSL_RNG_SEED: Random number generator initialization
gsl_sf_result: The gsl_sf_result struct
gsl_sf_result_e10: The gsl_sf_result struct
Gumbel distribution (Type 1): The Type-1 Gumbel Distribution
Gumbel distribution (Type 2): The Type-2 Gumbel Distribution

H
Haar wavelets: DWT Initialization
Hankel transforms, discrete: Discrete Hankel Transforms
HAVE_INLINE: Inline functions
hazard function, normal distribution: Probability functions
HBOOK: Ntuple References and Further Reading
header files, including: Compiling and Linking
heapsort: Sorting
HEMM, Level-3 BLAS: Level 3 GSL BLAS Interface
HEMV, Level-2 BLAS: Level 2 GSL BLAS Interface
HER, Level-2 BLAS: Level 2 GSL BLAS Interface
HER2, Level-2 BLAS: Level 2 GSL BLAS Interface
HER2K, Level-3 BLAS: Level 3 GSL BLAS Interface
HERK, Level-3 BLAS: Level 3 GSL BLAS Interface
hermitian matrix, complex, eigensystem: Complex Hermitian Matrices
Hessenberg decomposition: Hessenberg Decomposition of Real Matrices
Hessenberg triangular decomposition: Hessenberg-Triangular Decomposition of Real Matrices
histogram statistics: Histogram Statistics
histogram, from ntuple: Histogramming ntuple values
histograms: Histograms
histograms, random sampling from: The histogram probability distribution struct
Householder linear solver: Householder solver for linear systems
Householder matrix: Householder Transformations
Householder transformation: Householder Transformations
Hurwitz Zeta Function: Hurwitz Zeta Function
HYBRID algorithm, unscaled without derivatives: Algorithms without Derivatives
HYBRID algorithms for nonlinear systems: Algorithms using Derivatives
HYBRIDJ algorithm: Algorithms using Derivatives
HYBRIDS algorithm, scaled without derivatives: Algorithms without Derivatives
HYBRIDSJ algorithm: Algorithms using Derivatives
hydrogen atom: Coulomb Functions
hyperbolic cosine, inverse: Elementary Functions
hyperbolic functions, complex numbers: Complex Hyperbolic Functions
hyperbolic integrals: Hyperbolic Integrals
hyperbolic sine, inverse: Elementary Functions
hyperbolic space: Legendre Functions and Spherical Harmonics
hyperbolic tangent, inverse: Elementary Functions
hypergeometric functions: Hypergeometric Functions
hypergeometric random variates: The Hypergeometric Distribution
hypot: Elementary Functions
hypot function, special functions: Circular Trigonometric Functions

I
I(x), Bessel Functions: Regular Modified Cylindrical Bessel Functions
i(x), Bessel Functions: Regular Modified Spherical Bessel Functions
identity matrix: Initializing matrix elements
identity permutation: Permutation allocation
IEEE exceptions: Setting up your IEEE environment
IEEE floating point: IEEE floating-point arithmetic
IEEE format for floating point numbers: Representation of floating point numbers
IEEE infinity, defined as a macro: Infinities and Not-a-number
IEEE NaN, defined as a macro: Infinities and Not-a-number
illumination, units of: Light and Illumination
imperial units: Imperial Units
Implicit Euler method: Stepping Functions
Implicit Runge-Kutta method: Stepping Functions
importance sampling, VEGAS: VEGAS
including GSL header files: Compiling and Linking
incomplete Beta function, normalized: Incomplete Beta Function
incomplete Fermi-Dirac integral: Incomplete Fermi-Dirac Integrals
incomplete Gamma function: Incomplete Gamma Functions
indirect sorting: Sorting objects
indirect sorting, of vector elements: Sorting vectors
infinity, defined as a macro: Infinities and Not-a-number
infinity, IEEE format: Representation of floating point numbers
info-gsl mailing list: Obtaining GSL
initial value problems, differential equations: Ordinary Differential Equations
initializing matrices: Initializing matrix elements
initializing vectors: Initializing vector elements
inline functions: Inline functions
integer powers: Power Function
integrals, exponential: Exponential Integrals
integration, numerical (quadrature): Numerical Integration
interpolation: Interpolation
interpolation, using Chebyshev polynomials: Chebyshev Approximations
inverse complex trigonometric functions: Inverse Complex Trigonometric Functions
inverse cumulative distribution functions: Random Number Distributions
inverse hyperbolic cosine: Elementary Functions
inverse hyperbolic functions, complex numbers: Inverse Complex Hyperbolic Functions
inverse hyperbolic sine: Elementary Functions
inverse hyperbolic tangent: Elementary Functions
inverse of a matrix, by LU decomposition: LU Decomposition
inverting a permutation: Permutation functions
Irregular Cylindrical Bessel Functions: Irregular Cylindrical Bessel Functions
Irregular Modified Bessel Functions, Fractional Order: Irregular Modified Bessel Functions - Fractional Order
Irregular Modified Cylindrical Bessel Functions: Irregular Modified Cylindrical Bessel Functions
Irregular Modified Spherical Bessel Functions: Irregular Modified Spherical Bessel Functions
Irregular Spherical Bessel Functions: Irregular Spherical Bessel Functions
iterating through combinations: Combination functions
iterating through multisets: Multiset functions
iterating through permutations: Permutation functions
iterative refinement of solutions in linear systems: LU Decomposition

J
J(x), Bessel Functions: Regular Cylindrical Bessel Functions
j(x), Bessel Functions: Regular Spherical Bessel Functions
Jacobi elliptic functions: Elliptic Functions (Jacobi)
Jacobi orthogonalization: Singular Value Decomposition
Jacobian matrix, fitting: Overview of Nonlinear Least-Squares Fitting
Jacobian matrix, ODEs: Defining the ODE System
Jacobian matrix, root finding: Overview of Multidimensional Root Finding

K
K(x), Bessel Functions: Irregular Modified Cylindrical Bessel Functions
k(x), Bessel Functions: Irregular Modified Spherical Bessel Functions
knots, basis splines: Constructing the knots vector
kurtosis: Higher moments (skewness and kurtosis)

L
Laguerre functions: Laguerre Functions
Lambert function: Lambert W Functions
Landau distribution: The Landau Distribution
LAPACK: Eigenvalue and Eigenvector References
Laplace distribution: The Laplace Distribution
ldexp: Elementary Functions
LD_LIBRARY_PATH: Shared Libraries
leading dimension, matrices: Matrices
least squares fit: Least-Squares Fitting
least squares fitting, nonlinear: Nonlinear Least-Squares Fitting
least squares troubleshooting: Troubleshooting
least squares, covariance of best-fit parameters: Computing the covariance matrix of best fit parameters
Legendre forms of elliptic integrals: Definition of Legendre Forms
Legendre functions: Legendre Functions and Spherical Harmonics
Legendre polynomials: Legendre Functions and Spherical Harmonics
length, computed accurately using hypot: Elementary Functions
length, computed accurately using hypot: Elementary Functions
Levenberg-Marquardt algorithms: Minimization Algorithms using Derivatives
Levin u-transform: Series Acceleration
Levy distribution: The Levy alpha-Stable Distributions
Levy distribution, skew: The Levy skew alpha-Stable Distribution
libraries, linking with: Linking programs with the library
libraries, shared: Shared Libraries
license of GSL: Introduction
light, units of: Light and Illumination
linear algebra: Linear Algebra
linear algebra, BLAS: BLAS Support
linear interpolation: Interpolation Types
linear regression: Linear regression
linear systems, refinement of solutions: LU Decomposition
linear systems, solution of: LU Decomposition
linking with GSL libraries: Linking programs with the library
LMDER algorithm: Minimization Algorithms using Derivatives
log1p: Elementary Functions
logarithm and related functions: Logarithm and Related Functions
logarithm of Beta function: Beta Functions
logarithm of combinatorial factor C(m,n): Factorials
logarithm of complex number: Elementary Complex Functions
logarithm of cosh function, special functions: Hyperbolic Trigonometric Functions
logarithm of double factorial: Factorials
logarithm of factorial: Factorials
logarithm of Gamma function: Gamma Functions
logarithm of Pochhammer symbol: Pochhammer Symbol
logarithm of sinh function, special functions: Hyperbolic Trigonometric Functions
logarithm of the determinant of a matrix: LU Decomposition
logarithm, computed accurately near 1: Elementary Functions
Logarithmic random variates: The Logarithmic Distribution
Logistic distribution: The Logistic Distribution
Lognormal distribution: The Lognormal Distribution
long double: Long double
low discrepancy sequences: Quasi-Random Sequences
Low-level CBLAS: GSL CBLAS Library
LU decomposition: LU Decomposition

M
macros for mathematical constants: Mathematical Constants
magnitude of complex number: Properties of complex numbers
mailing list archives: Further Information
mailing list for GSL announcements: Obtaining GSL
mailing list, bug-gsl: Reporting Bugs
mantissa, IEEE format: Representation of floating point numbers
mass, units of: Mass and Weight
mathematical constants, defined as macros: Mathematical Constants
mathematical functions, elementary: Mathematical Functions
Mathieu Function Characteristic Values: Mathieu Function Characteristic Values
Mathieu functions: Mathieu Functions
matrices: Vectors and Matrices
matrices: Matrices
matrices, initializing: Initializing matrix elements
matrices, range-checking: Accessing matrix elements
matrix determinant: LU Decomposition
matrix diagonal: Creating row and column views
matrix factorization: Linear Algebra
matrix inverse: LU Decomposition
matrix square root, Cholesky decomposition: Cholesky Decomposition
matrix subdiagonal: Creating row and column views
matrix superdiagonal: Creating row and column views
matrix, constant: Initializing matrix elements
matrix, identity: Initializing matrix elements
matrix, operations: BLAS Support
matrix, zero: Initializing matrix elements
max: Statistics
maximal phase, Daubechies wavelets: DWT Initialization
maximization, see minimization: One dimensional Minimization
maximum of two numbers: Maximum and Minimum functions
maximum value, from histogram: Histogram Statistics
mean: Statistics
mean value, from histogram: Histogram Statistics
Mills’ ratio, inverse: Probability functions
min: Statistics
minimization, BFGS algorithm: Multimin Algorithms with Derivatives
minimization, caveats: Minimization Caveats
minimization, conjugate gradient algorithm: Multimin Algorithms with Derivatives
minimization, multidimensional: Multidimensional Minimization
minimization, one-dimensional: One dimensional Minimization
minimization, overview: Minimization Overview
minimization, Polak-Ribiere algorithm: Multimin Algorithms with Derivatives
minimization, providing a function to minimize: Providing the function to minimize
minimization, simplex algorithm: Multimin Algorithms without Derivatives
minimization, steepest descent algorithm: Multimin Algorithms with Derivatives
minimization, stopping parameters: Minimization Stopping Parameters
minimum finding, Brent’s method: Minimization Algorithms
minimum finding, golden section algorithm: Minimization Algorithms
minimum of two numbers: Maximum and Minimum functions
minimum value, from histogram: Histogram Statistics
MINPACK, minimization algorithms: Algorithms using Derivatives
MINPACK, minimization algorithms: Minimization Algorithms using Derivatives
MISCFUN: Special Functions References and Further Reading
MISER monte carlo integration: MISER
Mixed-radix FFT, complex data: Mixed-radix FFT routines for complex data
Mixed-radix FFT, real data: Mixed-radix FFT routines for real data
Modified Bessel Functions, Fractional Order: Regular Modified Bessel Functions - Fractional Order
Modified Clenshaw-Curtis quadrature: Integrands with weight functions
Modified Cylindrical Bessel Functions: Regular Modified Cylindrical Bessel Functions
Modified Givens Rotation, BLAS: Level 1 GSL BLAS Interface
Modified Newton’s method for nonlinear systems: Algorithms using Derivatives
Modified Spherical Bessel Functions: Regular Modified Spherical Bessel Functions
Monte Carlo integration: Monte Carlo Integration
MRG, multiple recursive random number generator: Random number generator algorithms
MT19937 random number generator: Random number generator algorithms
multi-parameter regression: Multi-parameter fitting
multidimensional integration: Monte Carlo Integration
multidimensional root finding, Broyden algorithm: Algorithms without Derivatives
multidimensional root finding, overview: Overview of Multidimensional Root Finding
multidimensional root finding, providing a function to solve: Providing the multidimensional system of equations to solve
Multimin, caveats: Multimin Caveats
Multinomial distribution: The Multinomial Distribution
multiplication: Elementary Operations
multisets: Multisets
multistep methods, ODEs: Stepping Functions

N
N-dimensional random direction vector: Spherical Vector Distributions
NaN, defined as a macro: Infinities and Not-a-number
nautical units: Speed and Nautical Units
Negative Binomial distribution, random variates: The Negative Binomial Distribution
Nelder-Mead simplex algorithm for minimization: Multimin Algorithms without Derivatives
Newton algorithm, discrete: Algorithms without Derivatives
Newton algorithm, globally convergent: Algorithms using Derivatives
Newton’s method for finding roots: Root Finding Algorithms using Derivatives
Newton’s method for systems of nonlinear equations: Algorithms using Derivatives
Niederreiter sequence: Quasi-Random Sequences
NIST Statistical Reference Datasets: Fitting References and Further Reading
non-normalized incomplete Gamma function: Incomplete Gamma Functions
nonlinear equation, solutions of: One dimensional Root-Finding
nonlinear fitting, stopping parameters: Search Stopping Parameters for Minimization Algorithms
nonlinear functions, minimization: One dimensional Minimization
nonlinear least squares fitting: Nonlinear Least-Squares Fitting
nonlinear least squares fitting, overview: Overview of Nonlinear Least-Squares Fitting
nonlinear systems of equations, solution of: Multidimensional Root-Finding
nonsymmetric matrix, real, eigensystem: Real Nonsymmetric Matrices
Nordsieck form: Stepping Functions
normalized form, IEEE format: Representation of floating point numbers
normalized incomplete Beta function: Incomplete Beta Function
Not-a-number, defined as a macro: Infinities and Not-a-number
NRM2, Level-1 BLAS: Level 1 GSL BLAS Interface
ntuples: N-tuples
nuclear physics, constants: Atomic and Nuclear Physics
numerical constants, defined as macros: Mathematical Constants
numerical derivatives: Numerical Differentiation
numerical integration (quadrature): Numerical Integration

O
obtaining GSL: Obtaining GSL
ODEs, initial value problems: Ordinary Differential Equations
optimization, combinatorial: Simulated Annealing
optimization, see minimization: One dimensional Minimization
optimized functions, alternatives: Alternative optimized functions
ordering, matrix elements: Matrices
ordinary differential equations, initial value problem: Ordinary Differential Equations
oscillatory functions, numerical integration of: QAWO adaptive integration for oscillatory functions
overflow, IEEE exceptions: Setting up your IEEE environment

P
Pareto distribution: The Pareto Distribution
PAW: Ntuple References and Further Reading
permutations: Permutations
physical constants: Physical Constants
physical dimension, matrices: Matrices
pi, defined as a macro: Mathematical Constants
plain Monte Carlo: PLAIN Monte Carlo
Pochhammer symbol: Pochhammer Symbol
Poisson random numbers: The Poisson Distribution
Polak-Ribiere algorithm, minimization: Multimin Algorithms with Derivatives
polar form of complex numbers: Representation of complex numbers
polar to rectangular conversion: Conversion Functions
polygamma functions: Psi (Digamma) Function
polynomial evaluation: Polynomial Evaluation
polynomial interpolation: Interpolation Types
polynomials, roots of: Polynomials
power function: Power Function
power of complex number: Elementary Complex Functions
power, units of: Thermal Energy and Power
precision, IEEE arithmetic: Setting up your IEEE environment
predictor-corrector method, ODEs: Stepping Functions
prefixes: Prefixes
pressure, units of: Pressure
Prince-Dormand, Runge-Kutta method: Stepping Functions
printers units: Printers Units
probability distribution, from histogram: The histogram probability distribution struct
probability distributions, from histograms: Resampling from histograms
projection of ntuples: Histogramming ntuple values
psi function: Psi (Digamma) Function

Q
QAG quadrature algorithm: QAG adaptive integration
QAGI quadrature algorithm: QAGI adaptive integration on infinite intervals
QAGP quadrature algorithm: QAGP adaptive integration with known singular points
QAGS quadrature algorithm: QAGS adaptive integration with singularities
QAWC quadrature algorithm: QAWC adaptive integration for Cauchy principal values
QAWF quadrature algorithm: QAWF adaptive integration for Fourier integrals
QAWO quadrature algorithm: QAWO adaptive integration for oscillatory functions
QAWS quadrature algorithm: QAWS adaptive integration for singular functions
QNG quadrature algorithm: QNG non-adaptive Gauss-Kronrod integration
QR decomposition: QR Decomposition
QR decomposition with column pivoting: QR Decomposition with Column Pivoting
QUADPACK: Numerical Integration
quadratic equation, solving: Quadratic Equations
quadrature: Numerical Integration
quantile functions: Random Number Distributions
quasi-random sequences: Quasi-Random Sequences

R
R250 shift-register random number generator: Other random number generators
Racah coefficients: Coupling Coefficients
Radial Mathieu Functions: Radial Mathieu Functions
radioactivity, units of: Radioactivity
Radix-2 FFT for real data: Radix-2 FFT routines for real data
Radix-2 FFT, complex data: Radix-2 FFT routines for complex data
rand, BSD random number generator: Unix random number generators
rand48 random number generator: Unix random number generators
random number distributions: Random Number Distributions
random number generators: Random Number Generation
random sampling from histograms: The histogram probability distribution struct
RANDU random number generator: Other random number generators
RANF random number generator: Other random number generators
range: Statistics
range-checking for matrices: Accessing matrix elements
range-checking for vectors: Accessing vector elements
RANLUX random number generator: Random number generator algorithms
RANLXD random number generator: Random number generator algorithms
RANLXS random number generator: Random number generator algorithms
RANMAR random number generator: Other random number generators
RANMAR random number generator: Other random number generators
Rayleigh distribution: The Rayleigh Distribution
Rayleigh Tail distribution: The Rayleigh Tail Distribution
real nonsymmetric matrix, eigensystem: Real Nonsymmetric Matrices
real symmetric matrix, eigensystem: Real Symmetric Matrices
Reciprocal Gamma function: Gamma Functions
rectangular to polar conversion: Conversion Functions
recursive stratified sampling, MISER: MISER
reduction of angular variables: Restriction Functions
refinement of solutions in linear systems: LU Decomposition
regression, least squares: Least-Squares Fitting
Regular Bessel Functions, Fractional Order: Regular Bessel Function - Fractional Order
Regular Bessel Functions, Zeros of: Zeros of Regular Bessel Functions
Regular Cylindrical Bessel Functions: Regular Cylindrical Bessel Functions
Regular Modified Bessel Functions, Fractional Order: Regular Modified Bessel Functions - Fractional Order
Regular Modified Cylindrical Bessel Functions: Regular Modified Cylindrical Bessel Functions
Regular Modified Spherical Bessel Functions: Regular Modified Spherical Bessel Functions
Regular Spherical Bessel Functions: Regular Spherical Bessel Functions
Regulated Gamma function: Gamma Functions
relative Pochhammer symbol: Pochhammer Symbol
reporting bugs in GSL: Reporting Bugs
representations of complex numbers: Representation of complex numbers
resampling from histograms: Resampling from histograms
residual, in nonlinear systems of equations: Search Stopping Parameters for the multidimensional solver
residual, in nonlinear systems of equations: Search Stopping Parameters for Minimization Algorithms
reversing a permutation: Permutation functions
Riemann Zeta Function: Riemann Zeta Function
RK2, Runge-Kutta method: Stepping Functions
RK4, Runge-Kutta method: Stepping Functions
RKF45, Runge-Kutta-Fehlberg method: Stepping Functions
robust regression: Robust linear regression
root finding: One dimensional Root-Finding
root finding, bisection algorithm: Root Bracketing Algorithms
root finding, Brent’s method: Root Bracketing Algorithms
root finding, caveats: Root Finding Caveats
root finding, false position algorithm: Root Bracketing Algorithms
root finding, initial guess: Search Bounds and Guesses
root finding, Newton’s method: Root Finding Algorithms using Derivatives
root finding, overview: Root Finding Overview
root finding, providing a function to solve: Providing the function to solve
root finding, search bounds: Search Bounds and Guesses
root finding, secant method: Root Finding Algorithms using Derivatives
root finding, Steffenson’s method: Root Finding Algorithms using Derivatives
root finding, stopping parameters: Search Stopping Parameters
root finding, stopping parameters: Search Stopping Parameters for the multidimensional solver
roots: One dimensional Root-Finding
ROTG, Level-1 BLAS: Level 1 GSL BLAS Interface
rounding mode: Setting up your IEEE environment
Runge-Kutta Cash-Karp method: Stepping Functions
Runge-Kutta methods, ordinary differential equations: Stepping Functions
Runge-Kutta Prince-Dormand method: Stepping Functions

S
safe comparison of floating point numbers: Approximate Comparison of Floating Point Numbers
safeguarded step-length algorithm: Minimization Algorithms
sampling from histograms: Resampling from histograms
sampling from histograms: The histogram probability distribution struct
SAXPY, Level-1 BLAS: Level 1 GSL BLAS Interface
SCAL, Level-1 BLAS: Level 1 GSL BLAS Interface
schedule, cooling: Simulated Annealing algorithm
se(q,x), Mathieu function: Angular Mathieu Functions
secant method for finding roots: Root Finding Algorithms using Derivatives
selection function, ntuples: Histogramming ntuple values
series, acceleration: Series Acceleration
shared libraries: Shared Libraries
shell prompt: Conventions used in this manual
Shi(x): Hyperbolic Integrals
shift-register random number generator: Other random number generators
Si(x): Trigonometric Integrals
sign bit, IEEE format: Representation of floating point numbers
sign of the determinant of a matrix: LU Decomposition
simplex algorithm, minimization: Multimin Algorithms without Derivatives
simulated annealing: Simulated Annealing
sin, of complex number: Complex Trigonometric Functions
sine function, special functions: Circular Trigonometric Functions
single precision, IEEE format: Representation of floating point numbers
singular functions, numerical integration of: QAWS adaptive integration for singular functions
singular points, specifying positions in quadrature: QAGP adaptive integration with known singular points
singular value decomposition: Singular Value Decomposition
Skew Levy distribution: The Levy skew alpha-Stable Distribution
skewness: Higher moments (skewness and kurtosis)
slope, see numerical derivative: Numerical Differentiation
Sobol sequence: Quasi-Random Sequences
solution of linear system by Householder transformations: Householder solver for linear systems
solution of linear systems, Ax=b: Linear Algebra
solving a nonlinear equation: One dimensional Root-Finding
solving nonlinear systems of equations: Multidimensional Root-Finding
sorting: Sorting
sorting eigenvalues and eigenvectors: Sorting Eigenvalues and Eigenvectors
sorting vector elements: Sorting vectors
source code, reuse in applications: Code Reuse
special functions: Special Functions
Spherical Bessel Functions: Regular Spherical Bessel Functions
spherical harmonics: Legendre Functions and Spherical Harmonics
spherical random variates, 2D: Spherical Vector Distributions
spherical random variates, 3D: Spherical Vector Distributions
spherical random variates, N-dimensional: Spherical Vector Distributions
spline: Interpolation
splines, basis: Basis Splines
square root of a matrix, Cholesky decomposition: Cholesky Decomposition
square root of complex number: Elementary Complex Functions
standard deviation: Statistics
standard deviation, from histogram: Histogram Statistics
standards conformance, ANSI C: Using the library
Statistical Reference Datasets (StRD): Fitting References and Further Reading
statistics: Statistics
statistics, from histogram: Histogram Statistics
steepest descent algorithm, minimization: Multimin Algorithms with Derivatives
Steffenson’s method for finding roots: Root Finding Algorithms using Derivatives
stratified sampling in Monte Carlo integration: Monte Carlo Integration
stride, of vector index: Vectors
Student t-distribution: The t-distribution
subdiagonal, of a matrix: Creating row and column views
summation, acceleration: Series Acceleration
superdiagonal, matrix: Creating row and column views
SVD: Singular Value Decomposition
SWAP, Level-1 BLAS: Level 1 GSL BLAS Interface
swapping permutation elements: Accessing permutation elements
SYMM, Level-3 BLAS: Level 3 GSL BLAS Interface
symmetric matrix, real, eigensystem: Real Symmetric Matrices
SYMV, Level-2 BLAS: Level 2 GSL BLAS Interface
synchrotron functions: Synchrotron Functions
SYR, Level-2 BLAS: Level 2 GSL BLAS Interface
SYR2, Level-2 BLAS: Level 2 GSL BLAS Interface
SYR2K, Level-3 BLAS: Level 3 GSL BLAS Interface
SYRK, Level-3 BLAS: Level 3 GSL BLAS Interface
systems of equations, nonlinear: Multidimensional Root-Finding

T
t-distribution: The t-distribution
t-test: Statistics
tangent of complex number: Complex Trigonometric Functions
Tausworthe random number generator: Random number generator algorithms
Taylor coefficients, computation of: Factorials
testing combination for validity: Combination properties
testing multiset for validity: Multiset properties
testing permutation for validity: Permutation properties
thermal energy, units of: Thermal Energy and Power
time units: Measurement of Time
trailing dimension, matrices: Matrices
transformation, Householder: Householder Transformations
transforms, Hankel: Discrete Hankel Transforms
transforms, wavelet: Wavelet Transforms
transport functions: Transport Functions
traveling salesman problem: Traveling Salesman Problem
tridiagonal decomposition: Tridiagonal Decomposition of Real Symmetric Matrices
tridiagonal decomposition: Tridiagonal Decomposition of Hermitian Matrices
tridiagonal systems: Tridiagonal Systems
trigonometric functions: Trigonometric Functions
trigonometric functions of complex numbers: Complex Trigonometric Functions
trigonometric integrals: Trigonometric Integrals
TRMM, Level-3 BLAS: Level 3 GSL BLAS Interface
TRMV, Level-2 BLAS: Level 2 GSL BLAS Interface
TRSM, Level-3 BLAS: Level 3 GSL BLAS Interface
TRSV, Level-2 BLAS: Level 2 GSL BLAS Interface
TSP: Traveling Salesman Problem
TT800 random number generator: Other random number generators
two dimensional Gaussian distribution: The Bivariate Gaussian Distribution
two dimensional histograms: Two dimensional histograms
two-sided exponential distribution: The Laplace Distribution
Type 1 Gumbel distribution, random variates: The Type-1 Gumbel Distribution
Type 2 Gumbel distribution: The Type-2 Gumbel Distribution

U
u-transform for series: Series Acceleration
underflow, IEEE exceptions: Setting up your IEEE environment
uniform distribution: The Flat (Uniform) Distribution
units, conversion of: Physical Constants
units, imperial: Imperial Units
Unix random number generators, rand: Unix random number generators
Unix random number generators, rand48: Unix random number generators
unnormalized incomplete Gamma function: Incomplete Gamma Functions
unweighted linear fits: Least-Squares Fitting
usage, compiling application programs: Using the library

V
value function, ntuples: Histogramming ntuple values
Van der Pol oscillator, example: ODE Example programs
variance: Statistics
variance, from histogram: Histogram Statistics
variance-covariance matrix, linear fits: Fitting Overview
VAX random number generator: Other random number generators
vector, operations: BLAS Support
vector, sorting elements of: Sorting vectors
vectors: Vectors and Matrices
vectors: Vectors
vectors, initializing: Initializing vector elements
vectors, range-checking: Accessing vector elements
VEGAS Monte Carlo integration: VEGAS
viscosity, units of: Viscosity
volume units: Volume Area and Length

W
W function: Lambert W Functions
warning options: GCC warning options for numerical programs
warranty (none): No Warranty
wavelet transforms: Wavelet Transforms
website, developer information: Further Information
Weibull distribution: The Weibull Distribution
weight, units of: Mass and Weight
weighted linear fits: Least-Squares Fitting
Wigner coefficients: Coupling Coefficients

Y
Y(x), Bessel Functions: Irregular Cylindrical Bessel Functions
y(x), Bessel Functions: Irregular Spherical Bessel Functions

Z
zero finding: One dimensional Root-Finding
zero matrix: Initializing matrix elements
zero, IEEE format: Representation of floating point numbers
Zeros of Regular Bessel Functions: Zeros of Regular Bessel Functions
Zeta functions: Zeta Functions
Ziggurat method: The Gaussian Distribution

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