Extended hypergeometric functions of two and three variables

Praveen Agarwal; Junesang Choi; Shilpi Jain

doi:10.4134/CKMS.2015.30.4.403

Extended hypergeometric functions of two and three variables

Praveen Agarwal
, Junesang Choi
, Shilpi Jain

International College of Engineering
Dongguk University
Poornima College of Engineering

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

38 Scopus citations

Abstract

Extensions of some classical special functions, for example, Beta function B(x, y) and generalized hypergeometric functions _pF_q have been actively investigated and found diverse applications. In recent years, several extensions for B(x, y) and _pF_q have been established by many authors in various ways. Here, we aim to generalize Appell's hypergeometric functions of two variables and Lauricella's hypergeometric function of three variables by using the extended generalized beta type function B_p^(α,β;m) p (x, y). Then some properties of the extended generalized Appell's hypergeometric functions and Lauricella's hypergeometric functions are investigated.

Original language	English
Pages (from-to)	403-414
Number of pages	12
Journal	Communications of the Korean Mathematical Society
Volume	30
Issue number	4
DOIs	https://doi.org/10.4134/CKMS.2015.30.4.403
State	Published - 2015
Externally published	Yes

Keywords

Beta function
Extended generalized Appell's functions
Extended generalized Gauss hypergeometric functions
Extended generalized Lauricella's functions
Extended generalized beta functions
Mellin transform

Access to Document

10.4134/CKMS.2015.30.4.403

Cite this

@article{26ae1e64dac2492bbe3963b6d55ed81f,

title = "Extended hypergeometric functions of two and three variables",

abstract = "Extensions of some classical special functions, for example, Beta function B(x, y) and generalized hypergeometric functions pFq have been actively investigated and found diverse applications. In recent years, several extensions for B(x, y) and pFq have been established by many authors in various ways. Here, we aim to generalize Appell's hypergeometric functions of two variables and Lauricella's hypergeometric function of three variables by using the extended generalized beta type function Bp(α,β;m) p (x, y). Then some properties of the extended generalized Appell's hypergeometric functions and Lauricella's hypergeometric functions are investigated.",

keywords = "Beta function, Extended generalized Appell's functions, Extended generalized Gauss hypergeometric functions, Extended generalized Lauricella's functions, Extended generalized beta functions, Mellin transform",

author = "Praveen Agarwal and Junesang Choi and Shilpi Jain",

note = "Publisher Copyright: {\textcopyright} 2015 Korean Mathematical Society.",

year = "2015",

doi = "10.4134/CKMS.2015.30.4.403",

language = "English",

volume = "30",

pages = "403--414",

journal = "Communications of the Korean Mathematical Society",

issn = "1225-1763",

publisher = "Korean Mathematical Society",

number = "4",

}

TY - JOUR

T1 - Extended hypergeometric functions of two and three variables

AU - Agarwal, Praveen

AU - Choi, Junesang

AU - Jain, Shilpi

PY - 2015

Y1 - 2015

N2 - Extensions of some classical special functions, for example, Beta function B(x, y) and generalized hypergeometric functions pFq have been actively investigated and found diverse applications. In recent years, several extensions for B(x, y) and pFq have been established by many authors in various ways. Here, we aim to generalize Appell's hypergeometric functions of two variables and Lauricella's hypergeometric function of three variables by using the extended generalized beta type function Bp(α,β;m) p (x, y). Then some properties of the extended generalized Appell's hypergeometric functions and Lauricella's hypergeometric functions are investigated.

AB - Extensions of some classical special functions, for example, Beta function B(x, y) and generalized hypergeometric functions pFq have been actively investigated and found diverse applications. In recent years, several extensions for B(x, y) and pFq have been established by many authors in various ways. Here, we aim to generalize Appell's hypergeometric functions of two variables and Lauricella's hypergeometric function of three variables by using the extended generalized beta type function Bp(α,β;m) p (x, y). Then some properties of the extended generalized Appell's hypergeometric functions and Lauricella's hypergeometric functions are investigated.

KW - Beta function

KW - Extended generalized Appell's functions

KW - Extended generalized Gauss hypergeometric functions

KW - Extended generalized Lauricella's functions

KW - Extended generalized beta functions

KW - Mellin transform

UR - https://www.scopus.com/pages/publications/84949210181

U2 - 10.4134/CKMS.2015.30.4.403

DO - 10.4134/CKMS.2015.30.4.403

M3 - Article

AN - SCOPUS:84949210181

SN - 1225-1763

VL - 30

SP - 403

EP - 414

JO - Communications of the Korean Mathematical Society

JF - Communications of the Korean Mathematical Society

IS - 4

ER -

Extended hypergeometric functions of two and three variables

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this