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 = 4, are computed by a moment-based method using the routine sr_fermidirac(dig,32,100,4), where dig=220 has been determined by the routine dig_fermidirac(100,4,212,4,32). For the respective moments, see Section 5 of Walter Gautschi, "Variable-precision recurrence coefficients for nonstandard orthogonal polynomials", Numerical Algorithms 52 (2009), 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:
- Gautschi, W. (2016). 32-digit values of the first 100 recurrence coefficients for the Fermi-Dirac-type weight function with exponent r=4. Purdue University Research Repository. doi:10.4231/R708639Z
The dataset consists of one text file and five Matlab scripts.