32-digit values of the first 100 recurrence coefficients for orthogonal polynomials relative to the weight function w(x)=|x|^c*(1-x)^a*(1+x)^b on [-1,1], a=-1/2, b=3/2, c=-3/4, are computed by a 2-component discretization procedure. The routine run_dig_sgjacobi,m, using N=100, dig0=34, dd=2, nofdig=32, a=-1/2, b=3/2, c=-3/4, and the routine dig_sgjacobi.m, determine the number dig=36 of working digits needed and return the recurrence coefficients to 32 digits in the Nx2 array ab. The routine ab=sr_gjacobi(nofdig,N) evaluates in dig-digit arithmetic the first 100 recurrence coefficients directly, returning them in the array ab. The values of dig, a, b, c are global variables assigned and declared global, in the calling program. The software provided in this dataset allows generating an arbitrary number of recurrence coefficients to any desired precision, and for arbitrary parameters a > -1, b > -1, c > -1.

Researchers should cite this work as follows:

• Gautschi, W. (2017). 32-digit values of the first 100 recurrence coefficients for a generalized Jacobi weight function with Jacobi parameters -1/2, 3/2 and exponent -3/4. Purdue University Research Repository. doi:10.4231/R7833Q1F

  BibTex | EndNote

1. Computer Science
2. Computer Science (Dept)
3. Mathematics
4. Modification algorithms for orthogonal polynomials
5. Orthogonal polynomials
6. Walter Gautschi Archives
7. weight functions

The dataset consists of one text file and nine Matlab scripts.