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32-digit values of the first 100 recurrence coefficients for the weight function w(x)=x^(1/2)*exp(-x)*(x-1-log(x)) on [0,Inf] obtained from moments

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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^a*exp(-x)*(x-1-log(x)) on [0,Inf], a=1/2

Version 1.0 - published on 30 Nov 2016 doi:10.4231/R7JH3J5S - cite this Archived on 31 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^a*exp(-x)*(x-1-log(x)) on [0,Inf], a=1/2, are computed by a moment-based method using the routine sr_laglog(dig,32,100,1/2), where dig=124 has been determined by the routine dig_laglog(100,1/2,116,4,32). For the moments, see Section 2.1 in Walter Gautschi, "Gauss quadrature routines for two classes of logarithmic weight functions", Numerical Algorithms 55 (2010), 265-277, doi: 10.1007/s11075-010-9366-0 and Section 1 for an application. The software provided in this dataset allows generating an arbitrary number N of recurrence coefficients for arbitrary a > -1 as well as for different precisions.

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The dataset consists of one text file and four Matlab scripts.

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