Uniformly convergent expansions for the generalized hypergeometric functions p –1Fp and pFp
We derive a convergent expansion of the generalized hypergeometric function p−1 F p in terms of the Bessel functions 0 F 1 that holds uniformly with respect to the argument in any horizontal strip of the complex plane. We further obtain a convergent expansion of the generalized hypergeometric functi...
| Authors: | , , |
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| Format: | article |
| Status: | Versión aceptada para publicación |
| Publication Date: | 2020 |
| Country: | España |
| Institution: | Universidad Pública de Navarra |
| Repository: | Academica-e. Repositorio Institucional de la Universidad Pública de Navarra |
| OAI Identifier: | oai:academica-e.unavarra.es:2454/37317 |
| Online Access: | https://hdl.handle.net/2454/37317 |
| Access Level: | Open access |
| Keyword: | Generalized hypergeometric function Bessel function Kummer function Convergent expansions Uniform expansions |
| Summary: | We derive a convergent expansion of the generalized hypergeometric function p−1 F p in terms of the Bessel functions 0 F 1 that holds uniformly with respect to the argument in any horizontal strip of the complex plane. We further obtain a convergent expansion of the generalized hypergeometric function p F p in terms of the confluent hypergeometric functions 1 F 1 that holds uniformly in any right half-plane. For both functions, we make a further step forward and give convergent expansions in terms of trigonometric, exponential and rational functions that hold uniformly in the same domains. For all four expansions we present explicit error bounds. The accuracy of the approximations is illustrated by some numerical experiments. |
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