32-digit values of the first 100 recurrence coefficients for orthogonal polynomials relative to the weight function w(x)=x^{1/2}/(exp(x)-1) on [0,Inf] are computed by a moment-based method using the routine sr_theodorus(dig,32,100), where dig=124 has been determined by the routine dig_theodorus(100,116,4,32). For the respective moments, see Section 4.2 of Walter Gautschi, "The spiral of Theodorus, numerical analysis, and special functions," Journal of Computational and Applied Mathematics 235 (2010), 1042-1052. doi: 10.1016/j.cam.2009.11.054. The software in this dataset allows generating an arbitrary number N of recurrence coefficients to any precision.

Researchers should cite this work as follows:

• Walter Gautschi (2016). 32-digit values of the first 100 recurrence coefficients for the Theodorus weight function. (Version 2.0). Purdue University Research Repository. doi:10.4231/R7CZ354Q

  BibTex | EndNote

1. Bose-Einstein distribution
2. Computer Science
3. Computer Science (Dept)
4. Equation Table
5. Gaussian quadrature
6. Mathematics
7. Moment problem
8. Numerical integrations
9. Orthogonal polynomials
10. Quadrature and cubature formulas
11. Slowly convergent series
12. Spiral of Theodorus
13. Summation of series
14. Walter Gautschi Archives

The version 2.0 of this dataset was supplemented by four Matlab scripts.