32-digit values of the first 100 recurrence coefficients for the weight function having an algebraic/logarithmic singularity 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(1/x)]^b on [0,1], a=1/2, b=3

Version 1.0 - published on 08 Dec 2016 doi:10.4231/R7H70CSK - cite this Archived on 09 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)=x^a*[log(1/x)]^b on [0,1], a = 1/2, b = 3, are computed by a moment-based method using the routine sr_l_alglog(dig,32,100,1/2,3), where dig = 176 has been determined by the routine dig_l_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, 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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