### 30.1 Definitions

A Chebyshev series is stored using the following structure,

typedef struct
{
double * c; /* coefficients c[0] .. c[order] */
int order; /* order of expansion */
double a; /* lower interval point */
double b; /* upper interval point */
...
} gsl_cheb_series

The approximation is made over the range *[a,b]* using
`order`+1 terms, including the coefficient *c[0]*. The series
is computed using the following convention,

f(x) = (c_0 / 2) + \sum_{n=1} c_n T_n(x)

which is needed when accessing the coefficients directly.