32-digit values of the first 100 recurrence coefficients for orthogonal polynomials relative to the weight function w(x)=exp(-1/x) on [0,c], c=2/3, are computed by a general-purpose discretization procedure using the routine sr_radtrans_dis(32,100), where c=2/3 and dig=34 have to be entered when prompted. The value dig=34 has been determined by the routine dig_radtrans_dis(100,32,2,32). The software provided in this dataset allows generating an arbitrary number N of recurrence coefficients for an arbitrary parameter c > 0 as well as for different precisions. The polynomials here obtained are closely related to the radiative transfer polynomials in Section 4 of Martin J. Gander and Alan H. Karp, "Stable computation of high order Gauss quadrature rules using discretization for measures in radiation transfer", Journal of Quantitative Spectroscopy & Radiative Transfer 68 (2001), 213-223. The alpha-coefficients of the latter, as well as the first beta-coefficient, are obtained by dividing ours by c, and the remaining beta-coefficients by dividing ours by c^2. The results are in complete agreement with those produced by sr_radtrans_cheb.m (cf. doi: 10.4231/R7N014H9), but are obtained about six times more slowly.

Researchers should cite this work as follows:

• Gautschi, W. (2017). 32-digit values of the first 100 recurrence coefficients, obtained by discretization, for a radiative transfer weight function with parameter c=2/3. Purdue University Research Repository. doi:10.4231/R7CF9N35

  BibTex | EndNote

1. Computer Science
2. Computer Science (Dept)
3. Gauss quadrature rules
4. Mathematics
5. Modification algorithms for orthogonal polynomials
6. Orthogonal polynomials
7. Walter Gautschi Archives
8. weight functions

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