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Polynomials orthogonal with respect to exponential integrals

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Abstract

Moment-based methods and related Matlab software are provided for generating orthogonal polynomials and associated Gaussian quadrature rules having as weight function the exponential integral E ν of arbitrary positive order ν supported on the positive real line or on a finite interval [0,c], c>0. By using the symbolic capabilities of Matlab, allowing for variable-precision arithmetic, the codes provided can be used to obtain as many of the recurrence coefficients for the orthogonal polynomials as desired, to any given accuracy, by choosing d-digit arithmetic with d large enough to compensate for the underlying ill-conditioning.

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Authors and Affiliations

  1. Department of Computer Sciences, Purdue University, West Lafayette, IN, 47907-2066, USA

    Walter Gautschi

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  1. Walter Gautschi
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Correspondence to Walter Gautschi.

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Gautschi, W. Polynomials orthogonal with respect to exponential integrals. Numer Algor 70, 215–226 (2015). https://doi.org/10.1007/s11075-014-9943-8

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  • DOI: https://doi.org/10.1007/s11075-014-9943-8

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