Series identities and associated families of generating functions

Chen, Kung-Yu; Srivástava, H. M.

doi:10.1016/j.jmaa.2005.03.030

Cited by 19 publications

(11 citation statements)

References 9 publications

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“…For (24), setting x = 1/2 and ε = β/2 + 2 − i (i ∈ N 0 ) in ( 4) with the help of ( 13), similarly, we can obtain the identity (24). We omit the details.…”

Section: General Summation Formulas For the Kampé De Fériet Functionmentioning

confidence: 98%

Generalized Summation Formulas for the Kampé de Fériet Function

Choi

Milovanović

Rathie

2021

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By employing two well-known Euler’s transformations for the hypergeometric function 2F1, Liu and Wang established numerous general transformation and reduction formulas for the Kampé de Fériet function and deduced many new summation formulas for the Kampé de Fériet function with the aid of classical summation theorems for the 2F1 due to Kummer, Gauss and Bailey. Here, by making a fundamental use of the above-mentioned reduction formulas, we aim to establish 32 general summation formulas for the Kampé de Fériet function with the help of generalizations of the above-referred summation formulas for the 2F1 due to Kummer, Gauss and Bailey. Relevant connections of some particular cases of our main identities, among numerous ones, with those known formulas are explicitly indicated.

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“…For (24), setting x = 1/2 and ε = β/2 + 2 − i (i ∈ N 0 ) in ( 4) with the help of ( 13), similarly, we can obtain the identity (24). We omit the details.…”

Section: General Summation Formulas For the Kampé De Fériet Functionmentioning

confidence: 98%

Generalized Summation Formulas for the Kampé de Fériet Function

Choi

Milovanović

Rathie

2021

Axioms

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“…for n ∈ N 0 ) defined (for λ, ν ∈ C and in terms of the familiar Gamma function) by For m ∈ N, we find it to be convenient to abbreviate the array of m parameters Motivated essentially by several recent investigations dealing with (for example) series identities and their various applications (cf. [6,8]; see also [5] and the other references cited in each of these earlier works), we prove two doubleseries identities and apply these identities in order to deduce hypergeometric reduction formulas and generatingfunction relationships associated with the Srivastava-Daoust hypergeometric function in two variables, which is defined in Section 3 below.…”

Section: Introduction and Definitionsmentioning

confidence: 97%

Some double-series identities and associated generating-function relationships

Chen

Liu

Srivástava

2006

Applied Mathematics Letters

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“…( [3]. In the last section, we derive several families of bilateral generating functions for the multivariable Meixner polynomials and the generalized Lauricella functions.…”

Section: Introductionmentioning

confidence: 99%

The Meixner Polynomials in Several Variables

Özmen¹,

Erkuş-Duman²

2019

IJAPM

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The polynomials are applied in many areas of mathematics, for instance, continued fractions, operator theory, analytic functions, interpolation, approximation theory, numerical analysis, electrostatics, statistical quantum mechanics, special functions, number theory, combinatorics, stochastic processes. On the other hand, generating functions have a great importance in special functions theory. The present study deals with some new properties of the Meixner polynomials in several variables. Firstly, we obtained some results include various families of multilinear and multilateral generating functions for the Meixner polynomials in several variables. In the last section, we get a theorem that gives a bilateral generating functions for these polynomials and the Lauricella functions. Finally, we derive some corollaries of the last theorem.

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Series identities and associated families of generating functions

Cited by 19 publications

References 9 publications

Generalized Summation Formulas for the Kampé de Fériet Function

Generalized Summation Formulas for the Kampé de Fériet Function

Some double-series identities and associated generating-function relationships

The Meixner Polynomials in Several Variables

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