New asymptotic expansion and error bound for Stirling formula of reciprocal Gamma function
Fecha
2018Versión
Acceso abierto / Sarbide irekia
Tipo
Artículo / Artikulua
Versión
Versión aceptada / Onetsi den bertsioa
Impacto
|
10.7153/mia-2018-21-65
Resumen
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 ...
[++]
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. [--]
Materias
Reciprocal gamma function,
Asymptotic expansions,
Error bounds
Editor
Ele-Math
Publicado en
Mathematical Inequalities & Applications, vol 21, number 4 (2018), 957-965
Departamento
Universidad Pública de Navarra. Departamento de Ingeniería Matemática e Informática /
Nafarroako Unibertsitate Publikoa. Matematika eta Informatika Ingeniaritza Saila
Versión del editor
Entidades Financiadoras
This research was supported by the Spanish Ministry of Economía y Competitividad, project
MTM2014-52859. The Universidad Pública de Navarra is acknowledged by its financial support.