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

Yıl 2017, Cilt: 5 Sayı: 1, 57 - 63, 30.04.2017

Dinesh Kumar

https://doi.org/10.36753/mathenot.421484

Öz

Anahtar Kelimeler

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

Kaynakça

• [1] Chaudhry, M.A. and Zubair, S.M., Generalized incomplete gamma functions with applications. J. Comput. Appl. Math. 55 (1994), 99-124.
• [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] Gasper, G. and Rahman, M., Basic Hypergeometric Series. Cambridge University Press, Cambridge, 1990.
• [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] 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] Parmar, R.K., Extended τ -Hypergeometric functions and associated properties. Computes rendus Mathematique 353 (2015), no. 5, 421–426.
• [7] Rainville, E.D., Special Functions. Macmillan Company, New York, 1960; Reprinted by Chelsea Publishing Company, Bronx, New York, 1971.
• [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] 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] 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.
• [11] Virchenko, N., Kalla, S.L. and Al-Zamel, A., Some results on a generalized hypergeometric function. Integral Transforms and Special Functions, 12 (2001), no. 1, 89–100.