On some formulas for the Horn function H₇(a, b, b′; c; w, z)

Abstract

Some new relations for the Horn function $H_7(a,b,b^{\mathrm{\prime }};c;w,z)$ are obtained including differentiation, integration, reduction and summation formulas. Some generating functions for various special functions are given in terms of these Horn functions.

Keywords:

• Special functions
• Horn functions
• Appell functions
• Humbert functions
• hypergeometric functions
• differentiation
• integrals
• series

AMS Subject Classification:

• C33

Disclosure statement

No potential conflict of interest was reported by the author(s).