Description
32-digit values of the first 100 recurrence coefficients for orthogonal polynomials relative to the weight function w(x)=x^mu*exp(-x^nu) on [0,Inf], mu=0, nu=8, are computed by a moment-based method using the routine sr_hrfreud(dig,32,100,0,8), where dig=164 has been determined by the routine dig_hrfreud(100,0,8,156,4,32). For the respective moments, see Exercise 2.20(a) in Walter Gautschi,"Orthogonal polynomials in MATLAB. Exercises and solutions", Software, Environments, and Tools, SIAM, Philadelphia, PA, 2016. The software provided in this dataset allows generating an arbitrary number N of recurrence coefficients for arbitrary exponents mu > -1, nu > 0, as well as for different precisions.
Cite this work
Researchers should cite this work as follows:
- Gautschi, W. (2017). 32-digit values of the first 100 recurrence coefficients for the half-range Freud weight function with exponent 8. Purdue University Research Repository. doi:10.4231/R76D5R5W
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Notes
The dataset consists of one text file and four Matlab scripts.