Symbolic operational images and decomposition formulas for hypergeometric functions

Abstract

Based upon the classical derivative and integral operators we introduce a new operator which allows the derivation of new symbolic operational images for hypergeometric functions. By means of these symbolic operational images a number of decomposition formulas involving quadruple series are then found. Other closely-related results are also considered.

Some Properties of New Hypergeometric Functions in Four Variables

“…Here, in this section, we shall discuss some operational relations by means of the following operational formulas (see [3,20]):…”

Decomposition Formulas for Triple q-Hypergeometric Functions

“…The concept of decomposition formulas for multiple hypergeometric functions is well known from the articles by Hasanov et al [1] and Bin-Saad [2]. This paper follows the first one by using -analogues of 15 symbolic operator formulas.…”

“…Hasanov, Srivastava, and Turaev have published several other articles of this type and Bin-Saad [2] treated the fourvariable case. The interested reader might consult papers by Exton on this last theme.…”

On the Connections between Certain Class of New Quadruple and Known Triple Hypergeometric Series

“…x D denote the derivative operator and the inverse of the derivative, respectively (see, for example, [14], [1] and [2]).…”