Decomposition formulas for some triple hypergeometric functions

Abstract

With the help of some techniques based upon certain inverse pairs of symbolic operators, the authors investigate several decomposition formulas associated with Srivastava's hypergeometric functions H A , H B and H C in three variables. Many operator identities involving these pairs of symbolic operators are first constructed for this purpose. By means of these operator identities, as many as 15 decomposition formulas are then found, which express the aforementioned triple hypergeometric functions in terms of such simpler functions as the products of the Gauss and Appell hypergeometric functions. Other closely-related results are also considered briefly.

Symbolic operational images and decomposition formulas for hypergeometric functions

“…Their method based on certain inverse pairs of symbolic operators. The method of Burchnall and Chaundy is applied mutatis mutandis by a number of workers, for example, Pandey [12], Srivastava [17], Hasanov and Srivastava [7,8], Hasanov et al [9], Hasanov and Turaev [10], Singhal and Bhati [16] in order to derive expansion formulas involving Lauricella's triple functions F …”

Decomposition Formulas of Kampé de Fériets Double Hypergeometric Functions

“…It was started to study by Burchnall and Chaundy in 1940 for Appell's double hypergeometric functions (see [4,5]) and Chaundy [7]. Recently, it has been studying for various special functions by many mathematicians (see [1,3,[8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]). In particular, Hasanov and Srivastava [13,15] presented a number of decomposition formulas in terms of such simpler hypergeometric functions as the Gauss and Appell's functions and Choi-Hasanov [8] gave a formula of an analytic continuation of the Clausen hypergeometric function 3 F 2 as an application of their decomposition formula.…”

“…Recently, it has been studying for various special functions by many mathematicians (see [1,3,[8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]). In particular, Hasanov and Srivastava [13,15] presented a number of decomposition formulas in terms of such simpler hypergeometric functions as the Gauss and Appell's functions and Choi-Hasanov [8] gave a formula of an analytic continuation of the Clausen hypergeometric function 3 F 2 as an application of their decomposition formula. In [3], using the differential operator D and its inverse D −1 (defined as the integral operator and setting the lower limit to 0), Bin-Saad develops techniques to represent hypergeometric functions and their generalizations with several summation quantifiers.…”

Hypergeometric functions of three variables in terms of integral representations

“…Thus the reaming four possibility lead to the four Appell function of two variables Which are defined as Lauricella (1893) further generalized the four Appell functions to functions of variables and defined as Lauricella (1893) (10, p.114) introduced 14 complete hypergeometric functions of three variables and of second order, he denoted his triple hypergeometric functions by the symbols of which corresponding, respectively to the three variables Lauricella functions ( ) ( ) ( ) ( ) defined in [10,p.113]; see also [13, p.33,ct seq.] and [2]. Saran (1954) initiated a systematic study of ten of the triple hypergeometric function from lauricella's set.…”