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Year 2019, Volume: 2 Issue: 3, 199 - 205, 30.09.2019
https://doi.org/10.33434/cams.550192

Abstract

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).

On Extensions of Extended Gauss Hypergeometric Function

Year 2019, Volume: 2 Issue: 3, 199 - 205, 30.09.2019
https://doi.org/10.33434/cams.550192

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.

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).
There are 18 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Ahmed Ali Atash 0000-0001-7762-6341

Salem Saleh Barahmah This is me

Maisoon Ahmed Kulib This is me

Publication Date September 30, 2019
Submission Date April 6, 2019
Acceptance Date July 26, 2019
Published in Issue Year 2019 Volume: 2 Issue: 3

Cite

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 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.

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