Asymptotische Darstellungen der hypergeometrischen Funktion für grosse Parameter unterschiedlicher Grössenordnung

Abstract

Asymptotic representations of the hypergeometric function $F(a,b;c;z)$ are derived where $b$ and $c-b$ either constants or tend to infinity independently of one another provided that Re $b=O_L(1)$, Re $(c-b)=O_L(1)$ and $b=o(a^{1/2-\delta }),c=o(a^{1/2-\delta }),\delta >0$.