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

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By Walter Gautschi

Purdue University

32-digit values of the first 100 recurrence coefficients for the weight function (inverse Gaussian distribution) w(x)=const*x^d*exp(-b/x^a-c*x^a) on [0,Inf], const=exp(1)/√(2*π), a=1, b=c=1/2, d=-3/2

Version 1.0 - published on 14 Feb 2017 doi:10.4231/R7W66HSK - 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)/√2*π, a=1, b=c=1/2,d=-3/2, are computed by a moment-based method using the routine sr_exp_abcd(dig,32,100,1,1/2,1/2,-3/2), where dig=120 has been determined by the routine dig_exp_abcd(100,1,1/2,1/2,-3/2,112,4,32). 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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