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32-digit values of the first 100 recurrence coefficients for the half-range bimodal weight function with parameter ε=1

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By Walter Gautschi

Purdue University

32-digit values of the first 100 recurrence coefficients for the weight function w(x)=(x^2)*exp[-(x^2-1)^2/(4*ε)] on [0,Inf], ε=1

Version 1.0 - published on 13 Jan 2017 doi:10.4231/R73T9F6B - cite this Archived on 14 Feb 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)=(x^2)*exp[-(x^2-1)^2/(4*ε)] on [0,Inf], ε=1, are computed by a multicomponent discretization procedure using the routine sr_OPhrbimod(32,100), with dig=34, epsi=1 entered at the prompt. The value dig=34 has been determined by the routine dig_sOPbimod(100,32,2,32), attesting to the high stability of the procedure. (Both routines may take several hours to run.) The auxiliary routine xhrbimod.m uses Newton's method to compute a zero x*=sqrt(1+u*) of the equation w(x)=1/2, given a close estimate of u*. There are two such zeros, x_1* and x_2*, x_1* < x_2*, and corresponding estimates -1 and 3.5 for u*. The software provided in this dataset allows generating an arbitrary number N of recurrence coefficients for arbitrary ε > 0 as well as for different precisions.

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

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