32-digit values of the first 100 recurrence coefficients for a four-parameter exponential weight function with parameters a=1/3, b=c=1/2, d=-7/6

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By Walter Gautschi

Purdue University

32-digit values of the first 100 recurrence coefficients for the weight function w(x)=const*x^d*exp(-b/x^a-c*x^a), const=exp(1)/(3*√(2*pi)), a=1/3, b=c=1/2, d=-7/6

Version 1.0 - published on 14 Feb 2017 doi:10.4231/R7RF5S1T - cite this Archived on 15 Mar 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)=const*x^d*exp(-b/x^a-c*x^a) on [0,Inf], const=exp(1)/(3*√2*π), a=1/3, b=c=1/2,d=-7/6, are computed by a moment-based method using the routine sr_exp_abcd(dig,32,100,1/3,1/2,1/2,-7/6), where dig=88 has been determined by the routine dig_exp_abcd(100,1/3,1/2,1/2,-7/6 ,80,4,32). The software provided in this dataset allows generating an arbitrary number N of recurrence coefficients for arbitrary a > 0, b > 0, c > 0, d real, as well as for different precisions.

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The dataset contains a text file and four Matlab routines.

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