Parameter Derivatives of the Jacobi Polynomials and the Gaussian Hypergeometric Function.
Please always quote using this URN: urn:nbn:de:0297-zib-1440
- The paper's main result is a simple derivation rule for the Jacobi polynomials with respect to their parameters, i.e. for $\partial_{\alpha} P_n^{\alpha,\beta}$, and $\partial_{\beta} P_n^{\alpha,\beta}$. It is obtained via relations for the Gaussian hypergeometric function concerning parameter derivatives and integer shifts in the first two arguments. These have an interest on their own for further applications to continuous and discrete orthogonal polynomials. The study is motivated by a Galerkin method with moving weight, presents all proofs in detail, and terminates in a brief discussion of the generated polynomials.
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| Author: | Jochen Fröhlich |
|---|---|
| Document Type: | ZIB-Report |
| Date of first Publication: | 1994/06/10 |
| Series (Serial Number): | ZIB-Report (SC-94-15) |
| ZIB-Reportnumber: | SC-94-15 |
| Published in: | Appeared in: Integral Transforms and Special Functions 2 (1994) pp. 252-266 |
