Description
32-digit values of the first 65 recurrence coefficients for orthogonal polynomials relative to the weight function w(x)=x^(-1/2)*exp(-x)*log(1+1/x) on [0,1], are computed by a 2-component discretization method using the routine sr_explogalgm1half01(32,65), where dig=36 has to be entered when prompted by the routine. The number 36 of digits has been determined by the routine dig_explogalgm1half01(65,32,4,32). Both of these routines make use of the 200 recurrence coefficients for the weight function x^(-1/2)*log(1/x) on [0,1] provided in the dataset doi:10.4231/R7QJ7FB6. This is the reason why only 65 recurrence coefficients are produced in the present dataset. If more are desired, the dataset for x^(-1/2)*log(1/x) would have to be revised so as to generate sufficiently more than 200 recurrence coefficients.
Cite this work
Researchers should cite this work as follows:
- Gautschi, W. (2017). 32-digit values of the first 65 recurrence coefficients for orthogonal polynomials relative to a weight function on [0,1] containing an algebraic singularity with exponent -1/2 and exponential/logarithmic factors. Purdue University Research Repository. doi:10.4231/R7KS6PK1
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Notes
The dataset consists of two text files and ten Matlab scripts.