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=3, are computed by a moment-based method using the routine sr_boseeinstein(dig,32,100,3), where dig=200 has been determined by the routine dig_boseeinstein(100,3,192,4,32). 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-type weight function with exponent 3. (Version 2.0). Purdue University Research Repository. doi:10.4231/R7BZ640B
The version 2.0 of this dataset was supplemented by four Matlab scripts and an updated text file.