Algorithm 793: GQRAT - Gauss quadrature for rational functions
The concern here is with Gauss-type quadrature rules that are exact for a mixture of polynomials and rational functions, the latter being selected so as to simulate poles that may be present in the integrand. The underlying theory is presented as well as methods for constructing such rational Gauss formulae. Relevant computer routines are provided and applied to a number of examples, including Fermi-Dirac and Bose-Einstein integrals of interest in solid state physics.
construction of quadrature rules gaussian quadrature exact for rational functions generalized fermi-dirac and bose einstein integrals