Convergent expansions of the incomplete gamma functions in terms of elementary functions
We consider the incomplete gamma function γ(a,z) for Ra>0 and z∈C. We derive several convergent expansions of z−aγ(a,z) in terms of exponentials and rational functions of z that hold uniformly in z with Rz bounded from below. These expansions, multiplied by ez, are expansions of ezz−aγ(a,z) u...
| Authors: | , , |
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| Format: | article |
| Status: | Versión aceptada para publicación |
| Publication Date: | 2017 |
| 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:2454/31776 |
| Online Access: | https://hdl.handle.net/2454/31776 |
| Access Level: | Open access |
| Keyword: | Incomplete gamma functions Convergent expansions Uniform expansions |
| Summary: | We consider the incomplete gamma function γ(a,z) for Ra>0 and z∈C. We derive several convergent expansions of z−aγ(a,z) in terms of exponentials and rational functions of z that hold uniformly in z with Rz bounded from below. These expansions, multiplied by ez, are expansions of ezz−aγ(a,z) uniformly convergent in z with Rz bounded from above. The expansions are accompanied by realistic error bounds. |
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