[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).
On Extensions of Extended Gauss Hypergeometric Function
Year 2019,
Volume: 2 Issue: 3, 199 - 205, 30.09.2019
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.
[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).
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
Atash AA, Barahmah SS, Kulib MA. On Extensions of Extended Gauss Hypergeometric Function. Communications in Advanced Mathematical Sciences. September 2019;2(3):199-205. doi:10.33434/cams.550192
Chicago
Atash, Ahmed Ali, Salem Saleh Barahmah, and Maisoon Ahmed Kulib. “On Extensions of Extended Gauss Hypergeometric Function”. Communications in Advanced Mathematical Sciences 2, no. 3 (September 2019): 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
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, 2019, doi: 10.33434/cams.550192.
ISNAD
Atash, Ahmed Ali et al. “On Extensions of Extended Gauss Hypergeometric Function”. Communications in Advanced Mathematical Sciences 2/3 (September 2019), 199-205. https://doi.org/10.33434/cams.550192.
JAMA
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, 2019, pp. 199-05, doi:10.33434/cams.550192.
Vancouver
Atash AA, Barahmah SS, Kulib MA. On Extensions of Extended Gauss Hypergeometric Function. Communications in Advanced Mathematical Sciences. 2019;2(3):199-205.