On some formulas for the confluent Horn functions H₁₀^(c) (a; c; w, z) and H₁₁^(c) (a, c, c′; d; w, z)

Abstract

Some new relations for the confluent Horn functions $H_{10}^{(c)}(a;c;w,z)$ and $H_{11}^{(c)}(a,c,c^{\mathrm{\prime }};d;w,z)$ are obtained including differentiation and integration formulas, series and reduction 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).