Numerical Algorithms

, Volume 70, Issue 1, pp 215–226 | Cite as

Polynomials orthogonal with respect to exponential integrals

  • Walter Gautschi
Original Paper


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.


Orthogonal polynomials Exponential integrals Chebyshev algorithm Matlab software 

Mathematics Subject Classification (2010)

33C47 65D30 


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of Computer SciencesPurdue UniversityWest LafayetteUSA

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