Research Article

An Extension of the τ -Gauss Hypergeometric Functions and its Properties

Volume: 5 Number: 1 April 30, 2017
EN

An Extension of the τ -Gauss Hypergeometric Functions and its Properties

Abstract


Keywords

Generalized Gamma functions,Gauss’s hypergeometric function,Generalized Gauss hypergeometric function,Extended τ -hypergeometric function,Mellin transform,Fractional calculus operators

References

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  2. [2] Chaudhry M.A. and Zubair, S.M., On a class of incomplete Gamma functions with applications. CRC Press (Chapman and Hall), Boca Raton, FL, 2002.
  3. [3] Gasper, G. and Rahman, M., Basic Hypergeometric Series. Cambridge University Press, Cambridge, 1990.
  4. [4] Kumar, D. and Kumar, S., Fractional Calculus of the Generalized Mittag-Leffler Type Function. International Scholarly Research Notices 2014 (2014), Article ID 907432, 6 pages.
  5. [5] Kumar, D. and Saxena, R.K., Generalized fractional calculus of the M-Series involving F3 hypergeometric function. Sohag J. Math. 2 (2015), no. 1, 17–22.
  6. [6] Parmar, R.K., Extended τ -Hypergeometric functions and associated properties. Computes rendus Mathematique 353 (2015), no. 5, 421–426.
  7. [7] Rainville, E.D., Special Functions. Macmillan Company, New York, 1960; Reprinted by Chelsea Publishing Company, Bronx, New York, 1971.
  8. [8] Samko, S.G., Kilbas, A.A. and Marichev, O.I., Fractional Integrals and Derivatives, Theory and Applications. Gordon and Breach, Yverdon et alibi, 1993.
  9. [9] Srivastava, H.M., Çetinkaya, A. and Onur Kıymaz, İ, A Certain generalized Pochhammer symbol and its applications to hypergeometric functions. Appl. Math. Comput. 226 (2014), 484–491.
  10. [10] Srivastava, H.M. and Karlsson, P.W., Multiple Gaussian Hypergeometric Series. Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons. New York, Chichester, Brisbane and Toronto, 1985.
APA
Kumar, D. (2017). An Extension of the τ -Gauss Hypergeometric Functions and its Properties. Mathematical Sciences and Applications E-Notes, 5(1), 57-63. https://doi.org/10.36753/mathenot.421484
AMA
1.Kumar D. An Extension of the τ -Gauss Hypergeometric Functions and its Properties. Math. Sci. Appl. E-Notes. 2017;5(1):57-63. doi:10.36753/mathenot.421484
Chicago
Kumar, Dinesh. 2017. “An Extension of the τ -Gauss Hypergeometric Functions and Its Properties”. Mathematical Sciences and Applications E-Notes 5 (1): 57-63. https://doi.org/10.36753/mathenot.421484.
EndNote
Kumar D (April 1, 2017) An Extension of the τ -Gauss Hypergeometric Functions and its Properties. Mathematical Sciences and Applications E-Notes 5 1 57–63.
IEEE
[1]D. Kumar, “An Extension of the τ -Gauss Hypergeometric Functions and its Properties”, Math. Sci. Appl. E-Notes, vol. 5, no. 1, pp. 57–63, Apr. 2017, doi: 10.36753/mathenot.421484.
ISNAD
Kumar, Dinesh. “An Extension of the τ -Gauss Hypergeometric Functions and Its Properties”. Mathematical Sciences and Applications E-Notes 5/1 (April 1, 2017): 57-63. https://doi.org/10.36753/mathenot.421484.
JAMA
1.Kumar D. An Extension of the τ -Gauss Hypergeometric Functions and its Properties. Math. Sci. Appl. E-Notes. 2017;5:57–63.
MLA
Kumar, Dinesh. “An Extension of the τ -Gauss Hypergeometric Functions and Its Properties”. Mathematical Sciences and Applications E-Notes, vol. 5, no. 1, Apr. 2017, pp. 57-63, doi:10.36753/mathenot.421484.
Vancouver
1.Dinesh Kumar. An Extension of the τ -Gauss Hypergeometric Functions and its Properties. Math. Sci. Appl. E-Notes. 2017 Apr. 1;5(1):57-63. doi:10.36753/mathenot.421484