On Extensions of Extended Gauss Hypergeometric Function

Ahmed Ali Atash; Salem Saleh Barahmah; Maisoon Ahmed Kulib

doi:10.33434/cams.550192

EN

On Extensions of Extended Gauss Hypergeometric Function

Abstract

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

References

[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).

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Ahmed Ali Atash
0000-0001-7762-6341
Yemen

Salem Saleh Barahmah This is me
Yemen

Maisoon Ahmed Kulib This is me
Yemen

Publication Date

September 30, 2019

Submission Date

April 6, 2019

Acceptance Date

July 26, 2019

Published in Issue

Year 2019 Volume: 2 Number: 3

DOI

https://doi.org/10.33434/cams.550192

IZ

https://izlik.org/JA73AZ75RT

APA

Atash, A. A., Barahmah, S. S., & Kulib, M. A. (2019). On Extensions of Extended Gauss Hypergeometric Function. Communications in Advanced Mathematical Sciences, 2(3), 199-205. https://doi.org/10.33434/cams.550192

AMA

1.Atash AA, Barahmah SS, Kulib MA. On Extensions of Extended Gauss Hypergeometric Function. Communications in Advanced Mathematical Sciences. 2019;2(3):199-205. doi:10.33434/cams.550192

Chicago

Atash, Ahmed Ali, Salem Saleh Barahmah, and Maisoon Ahmed Kulib. 2019. “On Extensions of Extended Gauss Hypergeometric Function”. Communications in Advanced Mathematical Sciences 2 (3): 199-205. https://doi.org/10.33434/cams.550192.

EndNote

Atash AA, Barahmah SS, Kulib MA (September 1, 2019) On Extensions of Extended Gauss Hypergeometric Function. Communications in Advanced Mathematical Sciences 2 3 199–205.

IEEE

[1]A. A. Atash, S. S. Barahmah, and M. A. Kulib, “On Extensions of Extended Gauss Hypergeometric Function”, Communications in Advanced Mathematical Sciences, vol. 2, no. 3, pp. 199–205, Sept. 2019, doi: 10.33434/cams.550192.

ISNAD

Atash, Ahmed Ali - Barahmah, Salem Saleh - Kulib, Maisoon Ahmed. “On Extensions of Extended Gauss Hypergeometric Function”. Communications in Advanced Mathematical Sciences 2/3 (September 1, 2019): 199-205. https://doi.org/10.33434/cams.550192.

JAMA

1.Atash AA, Barahmah SS, Kulib MA. On Extensions of Extended Gauss Hypergeometric Function. Communications in Advanced Mathematical Sciences. 2019;2:199–205.

MLA

Atash, Ahmed Ali, et al. “On Extensions of Extended Gauss Hypergeometric Function”. Communications in Advanced Mathematical Sciences, vol. 2, no. 3, Sept. 2019, pp. 199-05, doi:10.33434/cams.550192.

Vancouver

1.Ahmed Ali Atash, Salem Saleh Barahmah, Maisoon Ahmed Kulib. On Extensions of Extended Gauss Hypergeometric Function. Communications in Advanced Mathematical Sciences. 2019 Sep. 1;2(3):199-205. doi:10.33434/cams.550192

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Abstract

On Extensions of Extended Gauss Hypergeometric Function

Abstract

Keywords

References

Details

Primary Language

Subjects

Journal Section

Authors

Publication Date

Submission Date

Acceptance Date

Published in Issue

DOI

IZ

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