Abstract

We give a simple proof of a relation obtained by Qi-Guo for the sum of the Lah numbers in terms of the confluent hypergeometric function. We deduce the hypergeometric version of a combinatorial identity obtained by Engbers-Stocker. Besides, we show an alternative deduction for the Rathie-Paris formula satisfied by the Gauss hypergeometric function

Keywords

Hypergeometric function, Petkovsek-Wilf-Zeilberger’s method, Lah numbers, Binomial coefficient, Incomplete Beta function.