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The QNG algorithm is a non-adaptive procedure which uses fixed Gauss-Kronrod-Patterson abscissae to sample the integrand at a maximum of 87 points. It is provided for fast integration of smooth functions.

- Function:
*int***gsl_integration_qng***(const gsl_function **`f`, double`a`, double`b`, double`epsabs`, double`epsrel`, double *`result`, double *`abserr`, size_t *`neval`) -
This function applies the Gauss-Kronrod 10-point, 21-point, 43-point and 87-point integration rules in succession until an estimate of the integral of

*f*over*(a,b)*is achieved within the desired absolute and relative error limits,`epsabs`and`epsrel`. The function returns the final approximation,`result`, an estimate of the absolute error,`abserr`and the number of function evaluations used,`neval`. The Gauss-Kronrod rules are designed in such a way that each rule uses all the results of its predecessors, in order to minimize the total number of function evaluations.