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].

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

  BibTex | EndNote

1. Computer Science
2. Computer Science (Dept)
3. Krylov-Pal'tsev weight function
4. Mathematics
5. Modification algorithms for orthogonal polynomials
6. Orthogonal polynomials
7. Walter Gautschi Archives
8. weight functions

The dataset consists of nine text files and nine Matlab scripts.