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 [-Inf,Inf], mu=0, nu=8 are computed by a moment-based method using the routine sr_freud(dig,32,100,0,8), where dig=92 has been determined by the routine dig_freud(100,0,8,84,4,32). For the respective moments, see Exercise 2.23(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 with arbitrary exponents mu > -1, nu > 0, as well as for different precisions.

Researchers should cite this work as follows:

• Walter Gautschi (2016). 32-digit values of the first 100 recurrence coefficients for the Freud weight function with exponent 8. (Version 2.0). Purdue University Research Repository. doi:10.4231/R7R78C5Q

  BibTex | EndNote

1. Computer Science
2. Computer Science (Dept)
3. Equation Table
4. Freud polynomials
5. Freud weight function
6. Gaussian quadrature
7. Mathematics
8. Matlab
9. OPQ routine
10. Orthogonal polynomials
11. Walter Gautschi Archives

The version 2.0 of this dataset was supplemented by four Matlab scripts and an updated text file.