32-digit values of the first 100 recurrence coefficients for orthogonal polynomials relative to the weight function w(x)=x^a*[log(1/x)]^2 on [0,1], a=-1/2, are computed by a modified-moment-based method using the routine sr_jaclogsq(dig,32,100,-1/2), where dig=40 has been determined by the routine dig_jaclogsq(100,-1/2,32,4,32). For the modified moments, see Section 3 in Walter Gautschi, "On certain slowly convergent series occurring in plate contact problems", Mathematics of Computation 57 (1991), 325-338. It appears that Table 2 in the Appendix of this reference is not entirely accurate: As many as six trailing digits of the twenty digits given are inconsistent with the results (judged more reliable) obtained by the software provided in this dataset. This software allows generating an arbitrary number N of recurrence coefficients for arbitrary a > -1 (not an integer) as well as for different precisions.
Cite this work
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)=x^(-1/2)*[log(1/x)]^2 on [0,1]. Purdue University Research Repository. doi:10.4231/R72J68T4
The dataset consists of one text file and four Matlab scripts.