32-digit values of the first 100 recurrence coefficients for a Gegenbauer weight function with parameter λ=4 multiplied by an exponential function with coefficient a=8

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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-x^2)^(λ-1/2)*exp(-a*x^2) on [-1,1], λ=4, a=8

Version 1.0 - published on 27 Feb 2017 doi:10.4231/R74J0C39 - cite this Archived on 28 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)=(1-x^2)^(λ-1/2)*exp(-a*x^2) on [-1,1], λ=4, a=8, are computed by a 1-component discretization procedure. The routine [ab,dig]=dig_sgegexp(100,34,2,32), using sgegexp.m, determines the number dig=36 of working digits needed and returns the recurrence coefficients to 32 digits in the Nx2 array ab. The routine ab=sr_gegexp(nofdig,N) evaluates in dig-digit arithmetic directly the first N recurrence coefficients, returning them in the array ab. The values of dig, lam, a must be entered when prompted by the routine.

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

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