A reduction formula for the Appell series F3 in two variables

J. C. Prajapati; J. Choi; B. P. Patel; P. Agarwal

doi:10.12988/ijma.2015.59219

A reduction formula for the Appell series F3 in two variables

J. C. Prajapati
, J. Choi
, B. P. Patel
, P. Agarwal

Marwadi Education Foundation Group of Institutions
Dongguk University
Sardar Patel University
International College of Engineering

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

A large number of double series in two variables, in association with the theory of hypergeometric series, have been classied and fully de- veloped with named after their discoverers, for example, Appell series and their con uent cases, and various generalizations of these series in two variables. Here, in this paper, by starting with the classical Beta function, we show how one can derive a (presumably) new and (poten- tially) useful reduction formula for the Appell series F3 in two variables. Among many things, some interesting special cases of our main result are considered and relevant connections of some results presented here with those earlier ones are also pointed out.

Original language	English
Pages (from-to)	2377-2385
Number of pages	9
Journal	International Journal of Mathematical Analysis
Volume	9
Issue number	45-48
DOIs	https://doi.org/10.12988/ijma.2015.59219
State	Published - 2015
Externally published	Yes

Keywords

Appell series
Beta function
Combinatorial identities
Double series manipulations
Gamma function
Generalized binomial series
Hypergeometric series
Pochhammer symbol

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10.12988/ijma.2015.59219

Cite this

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title = "A reduction formula for the Appell series F3 in two variables",

abstract = "A large number of double series in two variables, in association with the theory of hypergeometric series, have been classied and fully de- veloped with named after their discoverers, for example, Appell series and their con uent cases, and various generalizations of these series in two variables. Here, in this paper, by starting with the classical Beta function, we show how one can derive a (presumably) new and (poten- tially) useful reduction formula for the Appell series F3 in two variables. Among many things, some interesting special cases of our main result are considered and relevant connections of some results presented here with those earlier ones are also pointed out.",

keywords = "Appell series, Beta function, Combinatorial identities, Double series manipulations, Gamma function, Generalized binomial series, Hypergeometric series, Pochhammer symbol",

author = "Prajapati, \{J. C.\} and J. Choi and Patel, \{B. P.\} and P. Agarwal",

note = "Publisher Copyright: {\textcopyright} 2015 J. C. Prajapati, J. Choi, B. P. Patel, P. Agarwal.",

year = "2015",

doi = "10.12988/ijma.2015.59219",

language = "English",

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AU - Prajapati, J. C.

AU - Choi, J.

AU - Patel, B. P.

AU - Agarwal, P.

PY - 2015

Y1 - 2015

N2 - A large number of double series in two variables, in association with the theory of hypergeometric series, have been classied and fully de- veloped with named after their discoverers, for example, Appell series and their con uent cases, and various generalizations of these series in two variables. Here, in this paper, by starting with the classical Beta function, we show how one can derive a (presumably) new and (poten- tially) useful reduction formula for the Appell series F3 in two variables. Among many things, some interesting special cases of our main result are considered and relevant connections of some results presented here with those earlier ones are also pointed out.

AB - A large number of double series in two variables, in association with the theory of hypergeometric series, have been classied and fully de- veloped with named after their discoverers, for example, Appell series and their con uent cases, and various generalizations of these series in two variables. Here, in this paper, by starting with the classical Beta function, we show how one can derive a (presumably) new and (poten- tially) useful reduction formula for the Appell series F3 in two variables. Among many things, some interesting special cases of our main result are considered and relevant connections of some results presented here with those earlier ones are also pointed out.

KW - Appell series

KW - Beta function

KW - Combinatorial identities

KW - Double series manipulations

KW - Gamma function

KW - Generalized binomial series

KW - Hypergeometric series

KW - Pochhammer symbol

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SP - 2377

EP - 2385

JO - International Journal of Mathematical Analysis

JF - International Journal of Mathematical Analysis

IS - 45-48

ER -

A reduction formula for the Appell series F3 in two variables

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