Description
32-digit values of the first 100 recurrence coefficients for orthogonal polynomials relative to the weight function w(x)=x^(1/2)*log(e/x) on [0,1] are computed by a moment-based method using the routine sr_alglog(dig,32,100,1/2,1), where dig=180 has been determined by the routine dig_alglog(100,1/2,1,172,4.32). 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 singularities, with the same exponents, occur at the right endpoint, that is, if w(x)=(1-x)^a*[log(e/(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. (2017). 32-digit values of the first 100 recurrence coefficients for the weight function having an algebraic/scaled-logarithmic singularity at 0 with exponent a=1/2 and power b=1. Purdue University Research Repository. doi:10.4231/R7RV0KQJ
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Notes
The dataset consists of one text file and five Matlab scripts.