A New Generalization of Pochhammer Symbol and Its Applications

Abstract

In this paper, we introduce a new generalization of the Pochhammer symbol by means of the generalization of extended gamma function (4). Using the generalization of Pochhammer symbol, we give a generalization of the extended hypergeo-metric functions one or several variables. Also, we obtain various integral representations, derivative formulas and certain properties of these functions.

Keywords

• gamma function
• beta function
• pochhammer symbol
• gauss hypergeometric function
• confluent hypergeometric function
• appell hypergeometric functions
• humbert hypergeometric functions of two variables
• integral representations
• derivative formulas
• recurrence relation
• primary 33c20
• 33c60
• 33d70
• secondary 33c65
• 33c90