32-digit values of the first 100 recurrence coefficients for a generalized Jacobi weight function with Jacobi parameters -1/2, 3/2 and exponent -3/4

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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|^c*(1-x)^a*(1+x)^b on [-1,1], a=-1/2, b=3/2, c=-3/4

Version 1.0 - published on 10 Mar 2017 doi:10.4231/R7833Q1F - cite this Archived on 11 Apr 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)=|x|^c*(1-x)^a*(1+x)^b on [-1,1], a=-1/2, b=3/2, c=-3/4, are computed by a 2-component discretization procedure. The routine run_dig_sgjacobi,m, using N=100, dig0=34, dd=2, nofdig=32, a=-1/2, b=3/2, c=-3/4, and the routine dig_sgjacobi.m, determine the number dig=36 of working digits needed and return the recurrence coefficients to 32 digits in the Nx2 array ab. The routine ab=sr_gjacobi(nofdig,N) evaluates in dig-digit arithmetic the first 100 recurrence coefficients directly, returning them in the array ab. The values of dig, a, b, c are global variables assigned and declared global, in the calling program. The software provided in this dataset allows generating an arbitrary number of recurrence coefficients to any desired precision, and for arbitrary parameters a > -1, b > -1, c > -1.

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

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