Some Results on the v-Analogue of Gamma Function

  • İnci Ege Department of Mathematics, Aydın Adnan Menderes University, Aydın, Turkey
Keywords: Gamma function, digamma (psi) function, v-analogue of Gamma function, v-analogue of beta function, v-digamma (psi) function, Bohr-Mollerup type theorem


In this paper, some properties for the v-analogue of Gamma and digamma functions are investigated. Also, a celebrated Bohr-Mollerup type theorem related to the v-analogue of Gamma function is given. Furthermore, an expression for the v-digamma function is presented by using the v-analogue of beta function. Also, some limits for the v-analogue of Gamma and beta functions are given.


U. M. Abubakar and M. L. Kaurangini, New extension of beta, Gauss and confluent hypergeometric functions, Cumhuriyet Science Journal 42(3) (2021), 663-676.

G. E. Andrews, R. Askey and R. Roy, Special Functions, Cambridge University Press, 1999.

W. W. Bell, Special Functions for Scientists and Engineers, Courier Corporation, 2014.

R. Diaz and E. Pariguan, On hypergeometric functions and Pochhammer k-symbol, Divulgaciones Matematicas 15 (2007), 179-192.

R. Diaz and C. Teruel, q, k-Generalized Gamma and beta functions, Journal of Nonlinear Mathematical Physics 12(1) (2005), 118-134.

E. Djabang, K. Nantomah and M. Iddrisu, On a v-analogue of the Gamma function and some associated inequalities, Journal of Mathematical and Computational Science 11(1) (2020), 74-86.

P. Duren, Invitation to Classical Analysis, Vol. 17, Amer. Math. Soc., 2012.

P. Etingof, Mathematical ideas and notions of quantum field theory, Preprint (2002).

K. S. Gehlot and K. S. Nisar, Extension of two parameter Gamma, Beta functions and its properties, Applications and Applied Mathematics: An International Journal 15(3) (2020), Special Issue 6, 39-55.

I. M. Gel'fand and G. E. Shilov, Generalized Functions, Vol. 1, Academic Press, 1964.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, Academic Press, 2014.

T. Kim and D. S. Kim, Note on the degenerate Gamma function, Russian Journal of Mathematical Physics 27(3) (2020), 352-358.

V. Krasniqi, A limit for the k-Gamma and k-beta function, International Mathematical Forum 5(33) (2010), 1613-1617.

A. M. Legendre, Exercises De Calcul Integrals Sur Divers De Transcendantes Et Sur Les Quadratures, Vol. 1, Nabu Press, 2010.

K. Nantomah, E. Prempeh and S. B. Twum, On a (p, k)-analogue of the Gamma function and some associated inequalities, Moroccan Journal of Pure and Applied Analysis 2(2) (2016), 79-90.

W. Rudin, Principles of Mathematical Analysis, Vol. 3, New York: McGraw-Hill, 1964.

Z. M. Song and L. Yin, A new Bohr-Mollerup type theorem related to Gamma function with two parameters, International Journal of Open Problems in Computer Science and Mathematics 11(1) (2018), 1-5.

E. T. Whitacker and G. N. Watson, A Course of Modern Analysis, Cambridge University Press, 1952.

How to Cite
Ege, İnci. (2022). Some Results on the v-Analogue of Gamma Function. Earthline Journal of Mathematical Sciences, 10(1), 109-123.