On some formulas for the Appell function<i>F</i>₂(<i>a, b, b</i>′;<i>c, c</i>′;<i>w; z</i>)

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.