Polynomials orthogonal with respect to exponential integrals
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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.
KeywordsOrthogonal polynomials Exponential integrals Chebyshev algorithm Matlab software
Mathematics Subject Classification (2010)33C47 65D30
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- 1.Abramowitz, M., Stegun, I.A. (eds.): Handbook of Mathematical Functions with Formulas, Graphs, and Marthematical Tables, National Bureau of Standards, Appl. Math. Ser. 55, U. S. Government Printing Office, Washington. D. C. (1964)Google Scholar
- 5.Gautschi, W.: Orthogonal Polynomials: Computation and Approximation, Numerical Mathematics and Scientific Computation. Oxford University Press, Oxford (2004)Google Scholar