32-digit values of the first 100 recurrence coefficients for the Freud weight function with exponent 8

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By Walter Gautschi

Purdue University

32-digit values of the first 100 recurrence coefficients for the weight function w(x)=x^mu*exp(-x^nu) on [-Inf,Inf], mu=0, nu=8

Version 2.0 - published on 29 Nov 2016 doi:10.4231/R7R78C5Q - cite this Archived on 30 Dec 2016

Licensed under Attribution 3.0 Unported

Description

32-digit values of the first 100 recurrence coefficients for orthogonal polynomials relative to the weight function w(x)=x^mu*exp(-x^nu) on [-Inf,Inf], mu=0, nu=8 are computed by a moment-based method using the routine sr_freud(dig,32,100,0,8), where dig=92 has been determined by the routine dig_freud(100,0,8,84,4,32). For the respective moments, see Exercise 2.23(a) in Walter Gautschi, "Orthogonal polynomials in MATLAB: Exercises and Solutions", Software, Environments, and Tools, SIAM, Philadelphia, PA, 2016. The software provided in this dataset allows generating an arbitrary number N of recurrence coefficients with arbitrary exponents mu > -1, nu > 0, as well as for different precisions.

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Notes

The version 2.0 of this dataset was supplemented by four Matlab scripts and an updated text file.

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