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32-digit values of the first 200 recurrence coefficients for the weight function w(x)=[log(1/x)]^2 on [0,1]

By Walter Gautschi

32-digit values of the first 200 recurrence coefficients for the weight function w(x)=x^a*[log(1/x)]^b on [0,1], a=0, b=2

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Version 2.0 - published on 14 Aug 2017 doi:10.4231/R7W95769 - cite this Archived on 15 Sep 2017

Licensed under Attribution 3.0 Unported

Description

32-digit values of the first 200 recurrence coefficients for orthogonal polynomials relative to the weight function w(x)=x^a*[log(1/x)]^b on [0,1], a=0, b=2, are computed by a moment-based method using the routine sr_l_alglog(dig,32,200,0,2), where dig=328 has been determined by the routine dig_l_alglog(200,0,2,320,4,32). The software provided in this dataset allows generating an arbitrary number N of recurrence coefficients for arbitrary a > -1, b > -1, as well as for different precisions. If the singularities, with the same exponents, occur at the right endpoint, that is, if w(x)=(1-x)^a*[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. This dataset contains updated and improved text file.