A connection formula between double hypergeometric series Ψ₂ and Φ₃

Abstract

The Humbert confluent hypergeometric functions Φ₂, Φ₃ and Ψ₂ are considered. The connection Φ₃ with the function Ψ₂ is established. Representations for functions Φ₃, Ψ₂ as series with the Gauss function ₂ F ₁ are proposed. Some special values of Φ₂ and Ψ₂ are found in terms of the generalized hypergeometric function _p F _q .

Keywords:

• hypergeometric functions
• Kummer theorem
• Gauss hypergeometric series

AMS Subject Classification :

• 33C15
• 33C70

Acknowledgement

The author is thankful to Prof. Yu.A. Brychkov for valuable comments which led to the improvement of this paper.