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)]^2 on [0,1] are computed by a moment-based method using the routine sr_alglog(dig,32,100,1/2,2), where dig=180 has been determined by the routine dig_alglog(100,1/2,2,172,4,32). 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.

Researchers should cite this work as follows:

• Gautschi, W. (2017). 32-digit values of the first 100 recurrence coefficients for a weight function having an algebraic/scaled-logarithmic singularity at 0 with exponent a=1/2 and power b=2. Purdue University Research Repository. doi:10.4231/R7251G6V

  BibTex | EndNote

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 five Matlab scripts.