Ahmed Ali ATASH, Salem Saleh BARAHMAH, Maisoon Ahmed KULİB

On Extensions of Extended Gauss Hypergeometric Function

The aim of this paper is to introduce a new extensions of extended Gauss hypergeometric function. Certain integral representations, transformation and summation formulas for extended Gauss hypergeometric function are presented and some special cases are also discussed.

Keywords:

Extended hypergeometric function, Mittag-Leffler function,

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[1] H. M. Srivastava, P. W. Karlsson, Multiple Gaussian Hypergeometric Series, Halsted Press, New York, 1985.
[2] G. M. Mittag-Leffler, Sur la nouvelle function Ea(z), C. R. Acad. Sci. Paris, 137 (1903), 554–558.
[3] A. Wiman, Uber den fundamental Satz in der Theorie der Funktionen Ea(z), Acta Math., 29 (1905), 191–201.
[4] T. R. Prabhakar, A singuler integral equation with a generalized Mittag-Leffer function in the kernel, Yokohoma Math. J., 19 (1971), 7–15.
[5] A. A. Al-Gonah, W. K. Mohammed, A new extension of extended Gamma and Beta functions and their properties, J. Sci. Engrg. Res., 5(9) (2018), 257–270.
[6] P. Agarwal, Certain properties of the generalized Gauss hypergeometric functions, Appl. Math. Inform. Sci., 8(5)(2014), 2315–2320.
[7] P. Agarwal, J. Choi , S. Jain, Extended hypergeometric functions of two and three variables, Commun. Korean Math. Soc., 30(4) (2015), 403–414.
[8] M. Luo , G. V. Milovanovic, P. Agarwal, Some results on the extended beta and extended hypergeometric functions, Appl. Math. Comput., 248 (2014), 631–651.
[9] E. Ozergin, M.A. Ozarslan, A. Altin, Extension of gamma, beta and hypergeometric functions, J. Comp. and Appl. Math., 235 (2011), 4601–4610.
[10] P. I. Pucheta, A new extended Beta function, Int. J. Math. Appl, 5(3-C) (2017), 255–260.
[11] M. Shadab, S. Jabee, J. Choi, An extension of Beta function and its application, Far East J. Math. Sci., 103(1) (2018), 235–251.
[12] M. A. Chaudhry, A. Qadir, M. Rafique, S. M. Zubair, Extension of Euler’s Beta function, J. Comput. Appl. Math., 78 (1997) 19–32.
[13] M. A. Chaudhry, A. Qadir, H. M.Srivastava, R. B. Paris, Extended hypergeometric and confluent hypergeometric function, Appl. Math. Comput., 159 (2004), 589–602.
[14] J. Choi, A. K. Rathie, R. K. Parmar, Extension of extended Beta, Hypergeometric and confluent hypergeometric functions, Honam Math. J., 36(2)(2014), 357–385.
[15] G. Rahman, G. Kanwal, K. S. Nisar , A. Ghaffar, A new extension of Beta and hypergeometric functions, (2018), doi:10.20944/preprints201801.0074.v1.
[16] A. A. Atash, S. S. Barahmah, M. A. Kulib, On a new extensions of extended Gamma and Beta functions, Int. J. Stat. Appl. Math., 3(6) (2018), 14–18.
[17] S. S. Barahmah, Further generalized Beta function with three parameters Mittag-Leffler function, Earthline J. Math. Sci., 1 (2019), 41–49.
[18] E. D. Rainville, Special Functions, The Macmillan Company, New York, (1960).