Abstract
Asymptotic expansions of the hypergeometric function F(a, b, c; z) for |b| \to \infty where a, 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 F for a (complex) \to \infty are derived where b, c (c \neq 0, -1, -2,\dots) and z (z \neq 0 , |Arg (1- z) | < \pi are fixed complex numbers. By change of a and b appropriate asymptotic representations of F for |b| \to \infty are obtained.
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