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32-digit values of the first 100 recurrence coefficients for the Jacobi weight function on [0,1] with exponents -1/2 times a logarithmic factor

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By Walter Gautschi

Purdue University

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

Version 1.0 - published on 21 Oct 2016 doi:10.4231/R7FQ9TKW - 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)=(1-x)^a*x^b*log(1/x) on [0,1], a=b=-1/2, are computed by a moment-based method using the routine sr_jaclog(dig,32,100,-1/2,-1/2), where dig=180 has been determined by the routine dig_jaclog(100,-1/2,-1/2,172,4,32). For the moments, see Section 3.1 in Walter Gautschi, "Gauss quadrature routines for two classes of logarithmic weight functions", Numerical Algorithms 55 (2010), 265-277. doi: 10.1007/s11075-010-9366-0. 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.

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

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