Gauss quadrature routines for two classes of logarithmic weight functions

Authors:
Walter Gautschi
Affiliations:
Department of Computer Sciences, Purdue University, West Lafayette, USA 47907-2066
Venue:
Numerical Algorithms
Year:
2010

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Abstract

By means of the Matlab symbolic/variable-precision facilities, routines are developed that generate an arbitrary number of recurrence coefficients to any given precision for polynomials orthogonal with respect to weight functions of Laguerre and Jacobi type containing logarithmic factors. The vehicle used is a symbolic modified Chebyshev algorithm based on ordinary as well as modified moments, executed with sufficiently high precision. The results are applied to Gaussian quadrature of integrals involving weight functions of the type mentioned.