32-digits 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/R7XS5SC9 - 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=36 has been determined by the routine dig_jaclogsq(100,1/2,28,4,32). 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. The software provided in this dataset 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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