IJPAM: Volume 118, No. 3 (2018)

Title

$p$-$q$-$k$ GAMMA AND BETA FUNCTIONS
AND THEIR PROPERTIES

Authors

Kuldeep Singh Gehlot$^1$, Kwara Nantomah$^2$
$^1$Government College Jodhpur
JNV University Jodhpur
Rajasthan, 306401, INDIA
$^2$Department of Mathematics
Faculty of Mathematical Sciences
University for Development Studies
Navrongo Campus, P.O. Box 24, Navrongo, UE/R, GHANA

Abstract

In this paper we introduce the p-q-k Pochhammer Symbol(q-analogue of p-k Pochhammer Symbol). We construct p-q-k Gamma and Beta functions(q-analogue of p-k Gamma and Beta functions respectively). Also, we prove some properties similar to those satisfied by the classical Gamma and Beta functions.

History

Received: 2017-02-09
Revised: 2017-11-19
Published: April 10, 2018

AMS Classification, Key Words

AMS Subject Classification: 33B15, 33D05
Key Words and Phrases: p-q-k Pochhammer Symbol, p-q-k Gamma and Beta functions, Two Parameter Pochhammer Symbol, Two Parameter Gamma Function, Two Parameter Beta Function, q-analogue

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Bibliography

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G. Gasper, M. Rahman, Basic Hypergeometric Series, Cambridge University Press, Cambridge, 1990. DOI: 10.2277/0521833574

2
G. S. Gehlot, Two Parameter Gamma Function and its Properties, arXiv:1701.01052v1 [math.CA], (2017), 1-7.

3
A. M. Mathai, H. J. Haubold, Special Functions for Applied Scientists, Springer-Verlag, New York, 2008. DOI: 10.1007/978-0-387-75894-7

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R. Diaz, C. Teruel, $q,k$-Generalized gamma and beta functions, J. Nonlinear Math. Phys., 12 No. 1 (2005), 118-134. DOI: 10.2991/jnmp.2005.12.1.10

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6
K. Nantomah. E. Prempeh, S. B. Twum, On a $(p,k)$-analogue of the Gamma function and some associated Inequalities, Moroccan J. Pure and Appl. Anal., 2 No. 2 (2016), 79-90. DOI: 10.7603/s40956-016-0006-0

How to Cite?

DOI: 10.12732/ijpam.v118i3.3 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2018
Volume: 118
Issue: 3
Pages: 519 - 526


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