32-digit values of the first 100 recurrence coefficients for orthogonal polynomials relative to the weight function w(x)=(1-x)^a*x^b*log(1/x) on (0,1) are computed for a=-1/2, b=1/2 by a modified-moment-based method using the routine sr_jaclog1(dig,32,100,-1/2,1/2), where dig=40 has been determined by the routine dig_jaclog1(100,-1/2,1/2,32,4,32). For the respective modified moments, see Section 3 in Walter Gautschi, Gauss quadrature routines for two classes of logarithmic weight functions, Numerical Algorithms 55 (2010), 265-277, doi: 10.1007/s11075-010-9366-0. The software provided in this dataset allows generating an arbitrary number N of recurrence coefficients for arbitrary exponents a > -1, b > -1.
Cite this work
Researchers should cite this work as follows:
- Walter Gautschi (2016). 32-digit values of the first 100 recurrence coefficients for an algebraically/logarithmically singular weight function on (0,1). (Version 2.0). Purdue University Research Repository. doi:10.4231/R7862DD9
The version 2.0 was supplemented by five Matlab scripts.