32-digit values of the first 100 recurrence coefficients for orthogonal polynomials relative to the weight function w(x)=[1/(exp(x)+1)]^r on [0,Inf], r=1, are computed by a moment-based method using the routine sr_fermidirac(dig,32,100,1), where dig=124 has been determined by the routine dig_fermidirac(100,1,116,4,32). For the respective moments, see Section 5 of Walter Gautschi, Variable-precision recurrence coefficients for nonstandard orthogonal polynomials, Numerical Algorithms 52 (2009). pp. 409-418. doi: 10.1007/s11075-009-9283-2. The software in this dataset allows generating an arbitrary number N of recurrence coefficients for an arbitrary integer r > 0 as well as for different precisions.
Cite this work
Researchers should cite this work as follows:
- Walter Gautschi (2016). 32-digit values of the first 100 recurrence coefficients for the Fermi-Dirac weight function. (Version 2.0). Purdue University Research Repository. doi:10.4231/R7HQ3WW3
The Matlab scripts were added to the 2.0 version of the dataset.