Description
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 moment-based method using the routine sr_lalog(dig,32,100,-1/2), where dig=124 has been determined by the routine dig_laglog(100,-1/2,116,4,32). 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. For the moments, see Section 2.1 of 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.
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)*exp(-x)*(x-1-log(x)) on [0,Inf] obtained from moments. Purdue University Research Repository. doi:10.4231/R79P2ZMR
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Notes
The dataset consists of one text file and four Matlab scripts.