Publication:
New asymptotic expansion and error bound for Stirling formula of reciprocal Gamma function

Consultable a partir de

Date

2018

Director

Publisher

Ele-Math
Acceso abierto / Sarbide irekia
Artículo / Artikulua
Versión aceptada / Onetsi den bertsioa

Project identifier

MINECO//MTM2014-52859-P/ES/recolecta

Abstract

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.

Description

Keywords

Reciprocal gamma function, Asymptotic expansions, Error bounds

Department

Ingeniería Matemática e Informática / Matematika eta Informatika Ingeniaritza

Faculty/School

Degree

Doctorate program

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