New asymptotic expansion and error bound for Stirling formula of reciprocal Gamma function
Studying the problem about if certain probability measures are determinate by its moments [4, 8, 10] is useful to know the asymptotic behavior of the probability densities for large values of argument. This requires, previously, the knowledge of the asymptotic expansion of reciprocal Gamma function...
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2018 |
| País: | España |
| Institución: | Universidad Pública de Navarra |
| Repositorio: | Academica-e. Repositorio Institucional de la Universidad Pública de Navarra |
| OAI Identifier: | oai:academica-e.unavarra.es:2454/32068 |
| Acceso en línea: | https://hdl.handle.net/2454/32068 |
| Access Level: | acceso abierto |
| Palabra clave: | Reciprocal gamma function Asymptotic expansions Error bounds |
| Sumario: | Studying the problem about if certain probability measures are determinate by its moments [4, 8, 10] is useful to know the asymptotic behavior of the probability densities for large values of argument. This requires, previously, the knowledge of the asymptotic expansion of reciprocal Gamma function 1/Γ(z) when ℜz is large and ℑz is fixed [8]. Then, the well known Stirling formula for large |z| of the Gamma function Γ(z) or its reciprocal 1/Γ(z) is not appropriate for this problem. So, the main aim of this paper is to obtain a new asymptotic expansion for reciprocal Gamma function valid for large ℜz and establish a new explicit error bound for the first term of this expansion, that is, the Stirling formula. |
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