Some formulas for the Appell functionF1(a, b, b′;c; w, z)

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.