32-digit values of the first 100 recurrence coefficients for orthogonal polynomials relative to the weight function w(x)=x^(2*mu)*exp(-x^2) on [0,c], c=1, mu=0, are computed by a moment-based method using the routine sr_lower_subrange_ghermite(dig,32,100,1,0), where dig=184 has been determined by the routine dig_lower_subrange_ghermite(100,1,0,176,4,32). The software provided in this dataset allows generating an arbitrary number N of recurrence coefficients for arbitrary c>0, mu>-1/2, as well as for different precisions. The polynomials so obtained are closely related to what in quantum chemistry and quantum physics are known as Rys polynomials orhogonal on [-1,1] with respect to the weight function w(x)=exp(-c*x^2); cf. Table 2.2 in Bernard Shizgal, "Spectral methods in chemistry and physics: applications to kinetic theory and quantum mechanics", Scientific Computation, Springer, Dordrecht, 2015. Indeed, all alpha-coefficients of the (monic) Rys polynomials are those obtained here divided by c; the same holds for the first beta-coefficient, whereas the remaining beta-coefficients are those obtained here divided by c^2.

Researchers should cite this work as follows:

• Gautschi, W. (2016). 32-digit values of the first 100 recurrence coefficients for lower subrange generalized Hermite polynomials. Purdue University Research Repository. doi:10.4231/R7BV7DKM

  BibTex | EndNote

1. Computer Science
2. Computer Science (Dept)
3. Mathematics
4. Modification algorithms for orthogonal polynomials
5. Orthogonal polynomials
6. Subrange Hermite polynomials
7. Walter Gautschi Archives
8. weight functions

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