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32-digit values of the first 65 recurrence coefficients for the weight function w(x)=x^(-1/2)*exp(-x)*log(1+1/x) on [1,Inf]

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By Walter Gautschi

Purdue University

32-digit values of the first 65 recurrence coefficients for the weight function w(x)=x^a*exp(-x)*log(1+1/x) on [1,Inf], a=-1/2

Version 1.0 - published on 09 May 2017 doi:10.4231/R7ZW1HX0 - cite this Archived on 10 Jun 2017

Licensed under Attribution 3.0 Unported

Description

32-digit values of the first 65 recurrence coefficients for orthogonal polynomials relative to the weight function w(x)=x^a*exp(-x)*log(1+1/x) on [1,Inf], a=-1/2, are computed by a 1-component discretization method using the routine sr_explogalg1m1half_inf(32,65), where dig=36 has to be entered when prompted by the routine. The value 36 of dig has been determined by the routine dig_explogalg1m1half_inf(65,32,4,32). Both routines take many hours to run, the latter as much as 20 hours, the former about 16 hours. The software provided in this dataset allows generating any number N <= 65 of recurrence coefficients for any noninteger a > -1, as well as for different precisions.

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

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