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], a=1/2, b=1/2, are computed by a modified-moment-based method using the routine sr_jacobilog1(dig,32,100,1/2,1/2), where dig=34 has been determined by the routine dig_jacobilog1(100,1/2,1/2, 32,2,32), attesting to the high stability of the modified Chebyshev algorithm. The software provided in this dataset allows generating an arbitrary number N of recurrence coefficients for arbitrary a>-1, b>-1, as well as for different precisions. If the logarithmic singularity occurs at the right endpoint, that is, the logarithmic factor in w(x) is log(1/(1-x)), then the recurrence coefficients are 1-c_k, d_k, where c_k, d_k are the recurrence coefficients for the weight function (1-x)^b*x*a*log(1/x) on [0,1]. For the relevant modified moments, see Section 3.2 of Walter Gautschi, "Gauss quadrature routines for two classes of logarithmic weight functions", Numerical Algorithms 55 (2010), 265-277. doi: doi:10.1007/s11075-010-9366-0.

Researchers should cite this work as follows:

• Gautschi, W. (2016). 32-digit values of the first 100 recurrence coefficients for the weight function w(x)=(1-x)^(1/2)*x^(1/2)*log(1/x) on [0,1]. Purdue University Research Repository. doi:10.4231/R76W981N

  BibTex | EndNote

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

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