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32-digit values of the first 100 recurrence coefficients for symmetric subrange generalized Hermite polynomials

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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*mu)*exp(-x^2) on [-c,c], c=1, mu=0

Version 1.0 - published on 22 Nov 2016 doi:10.4231/R7GH9FX2 - cite this Archived on 23 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^(2*mu)*exp(-x^2) on [-c,c], c = 1, mu=0, are computed by a moment-based method using the routine sr_symm_subrange_ghermite(dig,32,100,1,0), where dig=108 has been determined by the routine dig_symm_subrange_ghermite(100,1,0,100,4,32). The software provided in this dataset allows generating an arbitrary number N of recurrence coefficients for arbitrary c > 0, mu>-1/2, as well as for different precisions. The polynomials so obtained are closely related to what in quantum chemistry and quantum physics are known as Rys polynomials orthogonal on [-1,1] with respect to the weight function w(x)=exp(-c*x^2); cf. Table 2.2 in Bernard Shizgal, "Spectral methods in chemistry and physics: applications to kinetic theory and quantum mechanics", Scientific Computation, Springer, Dordrecht, 2015. Indeed, all alpha-coefficients of the (monic) Rys polynomials are those obtained here divided by c; the same holds for the first beta-coefficient, whereas the remaining beta-coefficients are those obtained here divided by c^2.

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

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