32-digit values of the first 100 recurrence coefficients for orthogonal polynomials relative to the weight function w(x)=(1-x)^a*x^b*log(1/x) on [0,1], a=b=-1/2, are computed by a moment-based method using the routine sr_jaclog(dig,32,100,-1/2,-1/2), where dig=180 has been determined by the routine dig_jaclog(100,-1/2,-1/2,172,4,32). For the moments, see Section 3.1 in Walter Gautschi, "Gauss quadrature routines for two classes of logarithmic weight functions", Numerical Algorithms 55 (2010), 265-277. doi: 10.1007/s11075-010-9366-0. The software provided in this dataset allows generating an arbitrary number N of recurrence coefficients for arbitrary a > -1, b > -1, 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 Jacobi weight function on [0,1] with exponents -1/2 times a logarithmic factor. Purdue University Research Repository. doi:10.4231/R7FQ9TKW
The dataset consists of one text file and four Matlab scripts.