32-digit values of the first 65 recurrence coefficients for the Krylov-Pal'tsev weight function w(x)=exp(-x)*log(1+1/x) on [0,Inf] with exponent 0

Listed in Datasets

By Walter Gautschi

Purdue University

32-digit values of the first 65 recurrence coefficients for the Krylov-Pal'tsev weight function w(x)=x^a*exp(-x)*log(1+1/x) on [0,Inf], a=0

Version 1.0 - published on 10 May 2017 doi:10.4231/R7CZ3555 - cite this Archived on 11 Jun 2017

Licensed under Attribution 3.0 Unported

Description

32-digit values of the first 65 recurrence coefficients for orthogonal polynomials relative to the weight function w(x)=x^a*exp(-x)*log(1+1/x) on [0,Inf], a=0, are computed by a 2-component discretization method using the routine sr_explog(32), where dig=48 and a=0 have to be entered when prompted by the routine. The value 48 of dig has been determined by the routine dig_explog(32,4,32). The software provided in this dataset allows generating any number N <= 65 of recurrence coefficients for any nonnegative integer a, as well as for different precisions. The script GQF_explog.m, upon entering a=0 (twice) and dig=48 when prompted, uses the routine sr_explog.m to recompute to 32 digits the 10 Gaussian quadrature rules for the weight function w published to 15 digits in Table 4 (a=0) of Krylov, V.I. and R.R. Pal'tsev, "Tables for numerical integration of functions with logarithmic and power singularities" (Russian), Izdat. "Nauka i Tekhnika", Minsk, 1967. [English translation by the IPST staff, Israel Program for Scientific Translations, Jerusalem, 1971]

Cite this work

Tags

Notes

The dataset consists of eight text files, one eps file, and nine 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).