Certain Multiple Series Identities

2015

In this paper, we obtain solutions of some multiple series identities involving bounded multiple sequences. We also derive hypergeometric forms of these identities involving Kamp´ e de F´ eriet double hypergeometric

A remarkably large number of operational techniques have drawn the attention of several researchers in the study of sequence of functions and polynomials. In this sequel, here, we aim to introduce a new sequence of functions involving the generalized Multi-Index Mittag-Leffler function by using operational techniques. Some generating relations and finite summation formula of the sequence presented here are also considered.

Journal of Applied Mathematics, Statistics and Informatics, 2012

The main object of this paper is to derive a number of general double series identities and to apply each of these identities in order to deduce several hypergeometric reduction formulas for the Srivastava-Daoust double hypergeometric function. The results presented in this paper are based essentially upon some

arXiv: General Mathematics, 2019

Motivated by the substantial development of the special functions, we contribute to establish some rigorous results on the general series identities with bounded sequences and hypergeometric functions with different arguments, which are generally applicable in nature. For the application purpose, we apply our results to some functions e.g.

Global Journal of Mathematical Analysis, 2014

In this paper, making use of some well-known summation formulae and generating relations due to Qureshi, Khan and Pathan, an attempt has been made to establish some transformation formulae of ordinary hyper geometric series which are seemed to be new and in different form. We have also given some special cases.

Acta Mathematica Scientia, 2014

Using series iteration techniques, we derive a number of general double series identities and apply each of these identities in order to deduce several hypergeometric reduction formulas involving the Srivastava-Daoust double hypergeometric function. The results presented in this article are based essentially upon the hypergeometric summation theorems of Kummer and Dixon.

International Journal of Mathematical Analysis, 2016

Honam Mathematical Journal, 2015

The aim of this paper is to provide a new class of series identities in the form of four general results. The results are established with the help of generalizatons of the classical Kummer's summation theorem obtained earlier by Rakha and Rathie. Results obtained earlier by Srivastava, Bailey and Rathie et al. follow special cases of our main findings.

Symmetry

Due to the great success of hypergeometric functions of one variable, a number of hypergeometric functions of two or more variables have been introduced and explored. Among them, the Kampé de Fériet function and its generalizations have been actively researched and applied. The aim of this paper is to provide certain reduction, transformation and summation formulae for the general Kampé de Fériet function and Srivastava’s general triple hypergeometric series, where the parameters and the variables are suitably specified. The identities presented in the theorems and additional comparable outcomes are hoped to be supplied by the use of computer-aid programs, for example, Mathematica. Symmetry occurs naturally in p+1Fp, the Kampé de Fériet function and the Srivastava’s function F(3)[x,y,z], which are three of the most important functions discussed in this study.

Mathematical Sciences, 2015

In this paper, we use a general identity for generalized hypergeometric series to obtain some new applications. The first application is a hypergeometric-type decomposition formula for elementary special functions and the second one is a generalization of the well-known Euler identity e i x ¼ cos x þ i sin x and an extension of hyperbolic functions in the sequel. Applying the mentioned identity on classical hypergeometric orthogonal polynomials and deriving summation formulae for some classical summation theorems are two further applications of this identity.