32-digit values of the first 100 recurrence coefficients for the weight function w(x)=[(1-.999*x^2)*(1-x^2)]^(-1/2) on [-1,1]

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By Walter Gautschi

Purdue University

32-digit values of the first 100 recurrence coefficients for the weight function w(x)=((1-om2*x^2)*(1-x^2))^(-1/2) on [-1,1], om2=.999

Version 1.0 - published on 23 Nov 2016 doi:10.4231/R7N877RQ - cite this Archived on 24 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)=((1-om2*x^2)*(1-x^2))^(-1/2) on [-1,1], om2=.999, are computed by a modified-moment-based method using the routine sr_ellcheb(dig,32,100,.999), where dig=36 has been determined by the routine dig_ellcheb(100,.999,32,4,32), attesting to the high stability of the modified Chebyshev algorithm. (With the parameter om2 very close to 1, this routine will take some extra time to run.) For the modified moments, see Example 4.4 in Walter Gautschi, "On generating orthogonal polynomials", SIAM Journal on Statistical and Scientific Computing 3 (1982), 289-317. doi: 10.1137/0903018. The software provided in this dataset allows generating an arbitrary number N of recurrence coefficients for arbitrary parameter om2, 0 < om2 < 1, and for different precisions.

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

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