32-digit values of the first 100 recurrence coefficients for the Theodorus weight function

Listed in Datasets

By Walter Gautschi

Purdue University

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

Version 2.0 - published on 29 Nov 2016 doi:10.4231/R7CZ354Q - cite this Archived on 30 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)=x^{1/2}/(exp(x)-1) on [0,Inf] are computed by a moment-based method using the routine sr_theodorus(dig,32,100), where dig=124 has been determined by the routine dig_theodorus(100,116,4,32). For the respective moments, see Section 4.2 of Walter Gautschi, "The spiral of Theodorus, numerical analysis, and special functions," Journal of Computational and Applied Mathematics 235 (2010), 1042-1052. doi: 10.1016/j.cam.2009.11.054. The software in this dataset allows generating an arbitrary number N of recurrence coefficients to any precision.

Cite this work

Researchers should cite this work as follows:

Tags

Notes

The version 2.0 of this dataset was supplemented by four Matlab scripts.

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).