On some formulas for the Appell function<i>F</i><sub>2</sub>(<i>a, b, b</i>′;<i>c, c</i>′;<i>w; z</i>)
Yu. A. BrychkovA. A. Dorodnicyn Computing Center of the Russian Academy of Sciences, Vavilov str. 40, Moscow 119333, V-333, RussiaNasser SaadDepartment of Mathematics and Statistics, University of Prince Edward Island, Charlottetown, Prince Edward Island, Canada C1A 4P3
2013en
ABI
Abstract
New relations and transformation formulas for the Appell function F2 (a, b, b′; c, c′; w, z) and confluent Appell functions (Humbert functions) Ψ1, Ψ2 are obtained. These relations include limit formulas, integral representations, differentiation and recurrence formulas. Summation formulas for F2, Ψ1, and Ψ2 are derived.
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