New Extended Beta Function Definedby Product Of Two Wright Functions
Maisoon Kulib
1
(
Department of Mathematics, Faculty of Engineering, Aden University, Aden, Yemen.
)
Ahmed Al-Gonah
2
(
Department of Mathematics, Faculty of Science, Aden University, Aden, Yemen.
)
Keywords: Extended Beta function, Wright function, integral representations, summation formula, Tricomi function.,
Abstract :
This paper aims to introduce a new extension of extended Beta function by product of two Wright functions. Various properties of this extended function are investigated such as integral representations, summation formulas and Mellin transform.
[1] E. Ata, Generalized Beta Function Defined by Wright Function,available at:https://arXiv.org/abs/1803.031212.
[2] M. A.Chaudhry, A.Qadir,M.Rafique andS. M. Zubair, Extension of Euler's Beta function, Journal of Computational and Applied Mathematics.78 (1997) 19-32.
[3] J. Choi, A. K. Rathie, R. K. Parmar, Extension of extended Beta, Hypergeomettric andconfluent hypergeometric functions, Honam Mathematical Journal. 36 (2) (2014) 357- 385.
[4] G. Dattoli, , P.E. Ricci, I.Khomasuridze, M. Migliorati, Generating function involving arbitrary products, Tamsui Oxford Journal of Mathematical Sciences. 23 (3) (2007) 269-276.
[5] N. Dudi, U. M.Abubakar, A further Extension of Gamma and Beta Functions involving Generalized Mittag-Leffler Function and its Applications, Journal of Physical Sciences, 26 (2021) 61-71.
[6] A. Erd´elyi, W. Magnus, F. Oberhettinger, F.G.Tricomi, Higher Transcende-Ental Functions, Vol.1, McGraw-Hill, New York, Toronto, London, (1953).
[7] K.S. Gehlot, K.S. Nisar, Extension of two parameter Gamma, Beta functions and its properties, Applications and Applied mathematics: An international Journal (AAM), 15 (3) (2020) 39-55.
[8] M. A. Kulib, F. B. F. Mohsen, S. S. Barahmah, Further Extended Gamma and Betafunctions in terms of Generalized Wright function, Electronic Journal of university of Aden for Basic and Applied Sciences,1 (2) (2020) 77-83.
[9] M. A. Kulib, A. A. Al-Gonah, S. S. Barahmah. Certain investigations in the field of special functions, Journal of Mathematical Analysis and madding, 1(1) (2020) 87-98.
[10] Vandana Palsaniya, Ekta Mittal, Sunil Joshi and D.L. Suthar, A Note on the extended Beta function with its Application, Hindawi journal of mathematics volume 2021, Article ID 63537119,12 pages.
[11] E.D.Rainville, Special functions, Chelsea Pub.Com., New York, (1960).
[12] U. M.Abubakar, S. R. Kabara, New generalized extended Gamma and Beta functions with their applications, international Scientific Research and Innovation Congress, (2021) 446-465.
[13] R.Goyal, S.Momani, P.Agarwal, M.T.Raisa's, An extension of Beta by using Wiman’sfunction, Axiom, 10 (187) (2021) 1-11:http://dx.doi.org/10.3390/axiom1003087a.