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

Listed in Datasets

By Walter Gautschi

Purdue University

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=-1/2, b=1

Version 2.0 - published on 24 Apr 2017 doi:10.4231/R7QJ7FB6 - cite this Archived on 25 May 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=-1/2, b=1, are computed by a moment-based method using the routine sr_l_alglog(dig,32,200,-1/2,1), where dig=328 has been determined by the routine dig_l_alglog(200,-1/2,1,320,4,32). 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.

Cite this work

Researchers should cite this work as follows:

Tags

Notes

The dataset consists of one text file and four Matlab scripts. This is a revised and improved version of the dataset doi: 10.4231/R7BP00RH.

The Purdue University Research Repository (PURR) is a university core research facility provided by the Purdue University Libraries, the Office of the Executive Vice President for Research and Partnerships, and Information Technology at Purdue (ITaP).