UNIFORM ASYMPTOTIC EXPANSIONS FOR HYPERGEOMETRIC FUNCTIONS WITH LARGE PARAMETERS I

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  • A. B. OLDE DAALHUIS
    School of Mathematics, King's Buildings, University of Edinburgh, Edinburgh EH9 3JZ, UK

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<jats:p>In this paper, we obtain an asymptotic expansion for the Gauss hypergeometric function<jats:sub>2</jats:sub>F<jats:sub>1</jats:sub>(a, b - λ; c + λ; -z), as |λ| → ∞. The expansion holds for fixed values of a, b, and c, and is uniformly valid for z in the domain | ph z| < π.</jats:p>

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