32-digit values of the first 63 recurrence coefficients for orthogonal polynomials relative to the weight function w(x)=x^a*exp(-x)*log(1+1/x) on [0,Inf], a=3, are computed by a 2-component discretization method using the routine sr_explog(32), where dig=44 and a=3 have to be entered when prompted by the routine. The value 44 of dig has been determined by the routine dig_explog(32,4,32). The software provided in this dataset allows generating any number N <= 63 of recurrence coefficients for any nonnegative integer a, as well as for different precisions. The script GQF_explog.m, upon entering a=3 and dig=44 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=3) 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 63 recurrence coefficients for the Krylov-Pal'tsev weight function on [0,Inf] with exponent 3. Purdue University Research Repository. doi:10.4231/R79Z92XF
The dataset consists of nine text files and nine Matlab scripts.