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

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

Version 1.0 - published on 21 Oct 2016 doi:10.4231/R72J68T4 - cite this Archived on 13 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*[log(1/x)]^2 on [0,1], a=-1/2, are computed by a modified-moment-based method using the routine sr_jaclogsq(dig,32,100,-1/2), where dig=40 has been determined by the routine dig_jaclogsq(100,-1/2,32,4,32). For the modified moments, see Section 3 in Walter Gautschi, "On certain slowly convergent series occurring in plate contact problems", Mathematics of Computation 57 (1991), 325-338. It appears that Table 2 in the Appendix of this reference is not entirely accurate: As many as six trailing digits of the twenty digits given are inconsistent with the results (judged more reliable) obtained by the software provided in this dataset. This software allows generating an arbitrary number N of recurrence coefficients for arbitrary a > -1 (not an integer) 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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