Some formulas for the Appell function<i>F</i>₁(<i>a, b, b</i>′;<i>c; w, z</i>)

Abstract

Some new relations for the Appell function F 1 (a, b, b′; c; w, z) are obtained including differentiation and integration formulas, integral representations, series and recurrence relations. Some integrals are given which can be expressed in terms of F 1 and confluent Appell functions (Humbert functions) Φ1, Φ2, Φ3.