32-digit values of the first 100 recurrence coefficients for a half-range Binet-like weight function

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By Walter Gautschi

Purdue University

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

Version 1.0 - published on 24 May 2017 doi:10.4231/R7736NX3 - cite this Archived on 25 Jun 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)=log(1+exp(-x)) on [0,Inf] are computed by a 1-component discretization procedure using the routine sr_log1pe_0Inf(32,100), where dig=284 must be entered when prompted by the routine. The value 284 of dig has been determined by the routine dig_log1pe_0Inf(100,280,4,32). It is that large because of apparent instabilities in the discretization process. Both routines, sr_log1pe_0Inf.m and dig_log1pe_0Inf.m, may take many hours to run, the latter as many as 19 hours, the former about 10 hours. The software in this dataset allows generating an arbitrary number N of recurrence coefficients to any precision.

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The dataset consists of one text file and seven Matlab scripts.

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