32-digit values of the first 100 recurrence coefficients for the Fermi-Dirac-type weight function with exponent r=3

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By Walter Gautschi

Purdue University

32-digit values of the first 100 recurrence coefficients for orthogonal polynomials relative to the weight function w(x)=[1/(exp(x)+1)]^r on [0,Inf], r=3

Version 1.0 - published on 13 Jan 2017 doi:10.4231/R7VH5KT8 - cite this Archived on 13 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)=[1/(exp(x)+1)]^r on [0,Inf], r=3, are computed by a moment-based method using the routine sr_fermidirac(dig,32,100,3), where dig=196 has been determined by the routine dig_fermidirac(100,3,188,4,32). For the respective moments, see Section 5 of Walter Gautschi, "Variable-precision recurrence coefficients for nonstandard orthogonal polynomials", Numerical Algorithms 52 (2009), 409-418. doi:10.1007/s11075-009-9283-2. The software in this dataset allows generating an arbitrary number N of recurrence coefficients for an arbitrary integer r > 0 as well as for different precisions.

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

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