32-digit values of the first 100 recurrence coefficients for orthogonal polynomials relative to the weight function w(x)=c*K_nu(x) on [0,Inf], c=2cos(nu*pi/2)/pi, are computed for nu=1/3 by a moment-based method using the routine sr_modbess(dig,32,100,1/3), where dig=124 has been determined by the routine dig_modbess(100,1/3,116,4,32). For the respective moments, see Section 4.1 in Walter Gautschi, "Computation of Bessel and Airy functions and of related Gaussian quadrature formulae", BIT 42 (2002), 110-118. doi: doi:10.1023/A:1021974203359. The software provided in this dataset allows generating an arbitrary number N of recurrence coefficients for arbitrary order nu>0 (not an integer) in w(x) and 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 a modified Bessel weight function. (Version 2.0). Purdue University Research Repository. doi:10.4231/R73F4MKN
The version 2.0 of this dataset was supplemented by four Matlab scripts and an updated text file.