32-digit values of the first 100 recurrence coefficients for a square-root-logarithmic weight function

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By Walter Gautschi

Purdue University

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

Version 1.0 - published on 06 Dec 2016 doi:10.4231/R7NZ85NT - cite this Archived on 07 Jan 2017

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)=[log(1/x)]^b on [0,1], b = 1/2, are computed by a moment-based method using the routine sr_l_alglog(dig,32,100,0,1/2), where dig = 180 has been determined by the routine dig_l_alglog(100,0,1/2,172,4,32). The software provided in this dataset allows generating an arbitrary number N of recurrence coefficients for arbitrary b > -1, as well as for different precisions. If the singularity, with the same exponent, occurs at the right endpoint, that is, if w(x)=[log(1/(1-x))]^b on [0,1], then the alpha-coefficients must be replaced by 1 minus the present ones, whereas the beta-coefficients remain the same.

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

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