Functional Relations Involving Saran's Hypergeometric Functions Feand F(3) (original) (raw)

Relationships between Saran ’ s Hypergeometric Functions

2012

By simply splitting the hypergeometric Saran function FE into eight parts, we show how some useful and generalized relations between FE and Srivastava’s hypergeometric function F (3) can be obtained. These main results are shown to be specialized to yield certain relations between functions 0F1, 1F1, 0F3, Ψ2, and their products including different combinations with different values of parameters and signs of variables.

New Generalized Hypergeometric Functions

Ikonion Journal of Mathematics

The classical Gauss hypergeometric function and the Kumar confluent hypergeometric function are defined using a classical Pochammer symbol , and a factorial function. This research paper will present a two-parameter Pochhammer symbol, and discuss some of its properties such as recursive formulae and integral representation. In addition, the generalized Gauss and Kumar confluent hypergeometric functions are defined using a two-parameter Pochhammer symbol and two-parameter factorial function and some of the properties of the new generalized hypergeometric functions were also discussed.

The incomplete Srivastava’s triple hypergeometric functions γHB and ΓHB

Filomat, 2016

Recently Srivastava et al. [26] introduced the incomplete Pochhammer symbols by means of the incomplete gamma functions ?(s,x) and ?(s,x), and defined incomplete hypergeometric functions whose a number of interesting and fundamental properties and characteristics have been investigated. Further, ?etinkaya [6] introduced the incomplete second Appell hypergeometric functions and studied many interesting and fundamental properties and characteristics. In this paper, motivated by the abovementioned works, we introduce two incomplete Srivastava?s triple hypergeometric functions ?HB and ?HB by using the incomplete Pochhammer symbols and investigate certain properties, for example, their various integral representations, derivative formula, reduction formula and recurrence relation. Various (known or new) special cases and consequences of the results presented here are also considered.