Reduction formulas for the Appell and Humbert functions

ABSTRACT

Representations are obtained for some special cases of the Appell functions $F_1$, $F_3$ and the Humbert functions ${\mathrm{\Phi }}_1,$ ${\mathrm{\Phi }}_2,$ ${\mathrm{\Xi }}_1,$ ${\mathrm{\Xi }}_2$ in terms of elementary and simpler special functions.

KEYWORDS:

• Appell functions
• Humbert functions
• special functions
• reduction

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• C33
• 33C77
• 33C70

Disclosure statement

No potential conflict of interest was reported by the author.