JournalszaaVol. 1, No. 3pp. 1–11

Asymptotische Darstellungen der hypergeometrischen Funktionen für grosse Werte eines Parameters

  • Eberhard Wagner

    Martin-Luther-Universität Halle-Wittenberg, Germany
Asymptotische Darstellungen der hypergeometrischen Funktionen für grosse Werte eines Parameters cover

Abstract

Asymptotic expansions of the hypergeometric function F(a,b,c;z)F(a, b, c; z) for b|b| \to \infty where a,c,za, c, z are fixed complex numbers given in well-known tables (e.g. Bateman/Erdélyi: Higher transcendental functions I. New York 1953) are incorrect. In the present paper asymptotic representations of the hypergeomctric function FF for aa (complex) \to \infty are derived where b,c(c0,1,2,)b, c (c \neq 0, -1, -2,\dots) and z(z0z (z \neq 0, |Arg (1z)<π(1- z) | < \pi are fixed complex numbers. By change of aa and bb appropriate asymptotic representations of FF for b|b| \to \infty are obtained.

Cite this article

Eberhard Wagner, Asymptotische Darstellungen der hypergeometrischen Funktionen für grosse Werte eines Parameters. Z. Anal. Anwend. 1 (1982), no. 3, pp. 1–11

DOI 10.4171/ZAA/16