32-digit values of the first 200 recurrence coefficients for orthogonal polynomials relative to the weight function w(x)=x^a* [log(1/x)]^b on [0,1], a=0, b=1, are computed by a moment-based method using the routine sr_l_alglog(dig,32,200,0,1), where dig=328 has been determined by the routine dig_l_alglog(200,0,1,320,4,32). The results are in agreement, except for occasional endfigure errors of 1 unit, with the first 20 recurrence coefficients given to 12 digits in Table 1 of Bernard Danloy, "Numerical construction of Gaussian quadrature formulas for int_0^1 (-Log x)*x^a*f(x)dx and int_0^Inf E_m(x)f(x)dx, Math. Comp. 27 (1973), 861-869. Use of the routine sgauss.m in the dataset doi:10.4231/R72805KQ also verified to the same accuracy the 10- and 20-point Gaussian quadrature formulae given in Table 2 of this reference.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(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.

Researchers should cite this work as follows:

• Walter Gautschi (2017). 32-digit values of the first 200 recurrence coefficients for the weight function w(x)=log(1/x) on [0,1]. (Version 2.0). Purdue University Research Repository. doi:10.4231/R7QN64RH

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

The dataset consists of one text file and four Matlab scripts. This versions enables 32-digit values of the first 200 recurrence coefficients for the weight function w(x)=log(1/x) on [0,1].