32-digit values of the first 65 recurrence coefficients for orthogonal polynomials relative to the weight function w(x)=x^a*exp(-x)*log(1+1/x) on [0,Inf], a=0, are computed by a 2-component discretization method using the routine sr_explog(32), where dig=48 and a=0 have to be entered when prompted by the routine. The value 48 of dig has been determined by the routine dig_explog(32,4,32). The software provided in this dataset allows generating any number N <= 65 of recurrence coefficients for any nonnegative integer a, as well as for different precisions. The script GQF_explog.m, upon entering a=0 (twice) and dig=48 when prompted, uses the routine sr_explog.m to recompute to 32 digits the 10 Gaussian quadrature rules for the weight function w published to 15 digits in Table 4 (a=0) of Krylov, V.I. and R.R. Pal'tsev, "Tables for numerical integration of functions with logarithmic and power singularities" (Russian), Izdat. "Nauka i Tekhnika", Minsk, 1967. [English translation by the IPST staff, Israel Program for Scientific Translations, Jerusalem, 1971]
Cite this work
Researchers should cite this work as follows:
- Gautschi, W. (2017). 32-digit values of the first 65 recurrence coefficients for the Krylov-Pal'tsev weight function w(x)=exp(-x)*log(1+1/x) on [0,Inf] with exponent 0. Purdue University Research Repository. doi:10.4231/R7CZ3555
The dataset consists of eight text files, one eps file, and nine Matlab scripts.