32-digit values of the first 100 recurrence coefficients for a weight function having an algebraic/scaled-logarithmic singularity at 0 with exponent a = -1/2 and power b=3

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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(e/x)]^b on [0,1], a=-1/2, b=3

Version 1.0 - published on 24 Apr 2017 doi:10.4231/R75X26Z9 - cite this Archived on 25 May 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)=x^(-1/2)*[log(e/x)]^3 on [0,1] are computed by a moment-based method using the routine sr_alglog(dig,32,100,-1/2,3), where dig=176 has been determined by the routine dig_alglog(100,-1/2,3,168,4,32). 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(e/(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 five Matlab scripts.

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