32-digit values of the first 100 recurrence coefficients for the Freud weight function with exponent 4

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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=4

Version 2.0 - published on 29 Nov 2016 doi:10.4231/R7VX0DHD - cite this Archived on 30 Dec 2016

Licensed under Attribution 3.0 Unported

Description

32-digit values of the first 100 beta coefficients for orthogonal polynomials relative to the weight function w(x)=x^μ*exp(-x^ν) on [-Inf,Inf], μ=0, ν=4 are computed by a moment-based method using the routine sr_freud(dig,32,100,0,4), where dig=84 has been determined by the routine dig_freud(100,0,4,76,4,32). 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 μ > -1, ν > 0, as well as for different precisions. In applications, the related weight function exp(-x^4/4) on [-Inf,Inf] is often used. Its recurrence coefficients can be obtained from ours simply by dividing all alpha-coefficients and the first beta-coefficient by 2 and dividing the remaining beta-coefficients by 2.

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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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