17 Numerical Integration

This chapter describes routines for performing numerical integration (quadrature) of a function in one dimension. There are routines for adaptive and non-adaptive integration of general functions, with specialised routines for specific cases. These include integration over infinite and semi-infinite ranges, singular integrals, including logarithmic singularities, computation of Cauchy principal values and oscillatory integrals. The library reimplements the algorithms used in QUADPACK, a numerical integration package written by Piessens, de Doncker-Kapenga, Ueberhuber and Kahaner. Fortran code for QUADPACK is available on Netlib. Also included are non-adaptive, fixed-order Gauss-Legendre integration routines with high precision coefficients by Pavel Holoborodko.

The functions described in this chapter are declared in the header file gsl_integration.h.