32-digit values of the first 100 recurrence coefficients for the weight function w(x)=x^(-1/2)*(1-x^3)^(-1/2) on [0,1]

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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^a*(1-x^c)^b on [0,1], a = -1/2, b = -1/2, c = 3

Version 1.0 - published on 15 Nov 2016 doi:10.4231/R7ST7MSG - cite this Archived on 16 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)=x^a* (1-x^c)^b on [0,1], a=-1/2, b=-1/2, c=3, are computed by a moment-based method using the routine sr_alg(dig,32,100,-1/2,-1/2,3), where dig=180 has been determined by the routine dig_alg(100,-1/2,-1/2,3,172,4,32). The results are in complete agreement with the first 26 recurrence coefficients given to 25 digits in Table 22 of Paul F. Byrd and David C. Galant, "Gauss quadrature rules involving some nonclassical weight functions", NASA Technical Note D-5785, National Aeronautics and Space Administration, Washington, D.C., 1970. The software provided in this dataset allows generating an arbitrary number N of recurrence coefficients for arbitrary a > -1/2, b -1/2, c > 0, as well as for different precisions.

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

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