On some formulas for the Appell function<i>F</i><sub>3</sub>(<i>a</i>,<i>a</i>′,<i>b</i>,<i>b</i>′;<i>c</i>;<i>w</i>,<i>z</i>)
Yu. A. BrychkovDorodnicyn 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
2015he
ABI
Abstract
New relations and transformation formulas for the Appell function F3(a,a′,b,b′;c;w;z) and the confluent Appell functions (Humbert functions) Φ2,Φ3,Ξ1,Ξ2 are obtained. These relations include limit formulas, integral representations, differentiation formulas. Various finite and infinite summation formulas are also derived.
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