32-digit values of the first 100 recurrence coefficients for orthogonal polynomials relative to the weight function w(x)=[log(1/x)]^b on [0,1], b = 1/2, are computed by a moment-based method using the routine sr_l_alglog(dig,32,100,0,1/2), where dig = 180 has been determined by the routine dig_l_alglog(100,0,1/2,172,4,32). The software provided in this dataset allows generating an arbitrary number N of recurrence coefficients for arbitrary b > -1, as well as for different precisions. If the singularity, with the same exponent, occurs at the right endpoint, that is, if w(x)=[log(1/(1-x))]^b on [0,1], then the alpha-coefficients must be replaced by 1 minus the present ones, whereas the beta-coefficients remain the same.
Cite this work
Researchers should cite this work as follows:
- Gautschi, W. (2016). 32-digit values of the first 100 recurrence coefficients for a square-root-logarithmic weight function. Purdue University Research Repository. doi:10.4231/R7NZ85NT
The dataset consists of one text file and four Matlab scripts.