32-digit values of the first 100 recurrence coefficients for orthogonal polynomials relative to the weight function w(x)=x^a*exp(-x)*(x-1-log(x)) on [0,Inf], a=1/2, are computed by a modified-moment-based method using the routine sr_laglogmm(dig,32,100,1/2), where dig=116 has been determined by the routine dig_laglogmm(100,1/2,108,4,32). For the modified moments, see Section 2.2 in Walter Gautschi, "Gauss quadrature routines for two classes of logarithmic weight functions", Numerical Algorithms 55 (2010), 265-277, doi: 10.1007/s11075-010-9366-0, and Section 1 for an application. The software provided in this dataset allows generating an arbitrary number N of recurrence coefficients for arbitrary a > -1 as well as for different precisions. See also doi:10.4231/R7JH3J5S for a method based on ordinary moments. Both methods produce the same answers, but the current one is about 60% faster to run.

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)*exp(-x)*(x-1-log(x)) on [0,Inf] obtained from modified moments. Purdue University Research Repository. doi:10.4231/R78P5XHT

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1. Computer Science
2. Gaussian quadrature
3. Logarithmic weight functions
4. Mathematics
5. Modification algorithms for orthogonal polynomials
6. Orthogonal polynomials
7. Walter Gautschi Archives

The dataset consists of one text file and five Matlab scripts.