32-digit values of the first 100 recurrence coefficients for orthogonal polynomials relative to the weight function w(x)=[x/(exp(x)-1)]^r on [0,Inf], r=1, are computed by a moment-based method using the routine sr_boseeinstein(dig,32,100,1), where dig=124 has been determined by the routine dig_boseeinstein(100,1,116,4,32). For the respective moments, see Section 4 in 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 provided in this dataset allows generating an arbitrary number N of recurrence coefficients for 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 Bose-Einstein weight function. (Version 2.0). Purdue University Research Repository. doi:10.4231/R7MG7MGF
The version 2.0 of this dataset was supplemented by four Matlab scripts and an updated text file.