Asymptotic expansions for generalized gamma and incomplete gamma functions

Abstract

Kobayashi(jour.phy.soc.japan 60(1991),1501_1512) considered a generalized Gamma function occuring in Diffraction Theory. This article considers a more general function involving Gauss hypergeometric function F(a,b;c,x)

Where that reduces to when p=1 and b=c.

The incomplete and the complementary incomplete functions associated with are introduced. Some properties and recurrence relations satisfied by these two functions are proved, and asymptotic expansions for the function and its associated incomplete and complementary incomplete functions are fully investigated.

Keywords:

• Asymptotic expansion
• gamma function
• recurrence relations.