Evaluation of some integral representations for extended Srivastava triple hypergeometric function HC,p,v(·)

Year 2019, Volume: 7 Issue: 1, 182 - 185, 15.04.2019

Showkat Ahmad Dar

Abstract

Many authors study some integral representations of the function $H_{C}(\cdot)$. Here, we obtain some integral representations for extended Srivastava triple hypergeometric function $H_{C,p,v}(\cdot)$ involving Meijer’s $G$-function of one variable, confluent hypergeometric and Whittaker functions.

Keywords

Srivastava's triple hypergeometric functions, Gauss hypergeometric function, Bessel function, Meijer’s $G$-function

References

• [1] Cuyt, A., Petersen, V., Verdonk, B.W., Waadeland, H. and Jones, W. B. ; Handbook of Continued Fractions for Special Functions. Springer Science+Business Media B.V., 2008.
• [2] Bozer, M. and Ozarslan, M. A. ; Notes on generalized gamma, beta and hypergeometric functions. J. Comput. Anal. Appl. 15(7), (2013), 1194-1201.
• [3] C¸ etinkaya,A., Yagbasana, M.,I. and Kiymaz, I.O. ; The Extended Srivastava’s Triple Hypergeometric Functions and Their Integral Representations. J. Nonlinear Sci. Appl., 2016, 1-1.
• [4] Choi, J.,Hasanov, A., Srivastava, H. M. and Turaev,M. ; Integral representations for Srivastava’s triple hypergeometric functions. Taiwanese J. Math. 15(6), (2011), 2751-2762.
• [5] Choi,J., Hasanov,A. and Turaev,M. ; Integral representations for Srivastava’s triple hypergeometric functions HC. Honam Mathematical J. 34(4), (2012) , 473-482.
• [6] Choi J., Rathie, A. K. and Parmar, R. k. ; Extension of extended Beta, hypergeometric function and confluent hypergeometric function. Honam Mathematical J., 36(2), 2014, 357-385.
• [7] Dar, S.A. and Paris, R.B., A (p;v)-extension of Srivastava’s triple hypergeometric function HC and its properties, Communicated.
• [8] Erdelyi, A., Magnus, W., Oberhettinger, F. and Tricomi, F. G. ; Higher Transcendental Functions. Vol. 1. McGraw-Hill, New york, Toronto and London, 1953.
• [9] Karlsson, P.W. ; Regions of convergences for hypergeometric series in three variables. Math. Scand, 48(1974), 241-248.
• [10] Luo, M. J., Milovanovic, G. V. and Agarwal,P. ; Some results on the extended beta and extended hypergeometric functions. Applied Mathematics and Computation , 248(2014) , 631-651.
• [11] Olver F. W. J., Lozier D. W., Boisvert R. F. and Clark C. W. (eds.); NIST Handbook of Mathematical Functions. Cambridge University Press, Cambridge, 2010.
• [12] O zergin,E., Ozarslan,M. A. and Altin,A. ; Extension of gamma, beta and hypergeometric functions. J. Comput. Appl. Math. 235(2011) , 4601-4610.
• [13] Parmar, R. K., Chopra, P. and Paris, R. B. ; On an Extension of Extended Beta and Hypergeometric Functions. arXiv:1502.06200 [math.CA], 22(2015).
• [14] Rainville, E. D. ; Special Functions. Macmillan Company, New York, 1960; Reprinted by Chelsea Publishing Company, Bronx, New York, 1971.
• [15] Srivastava,H.M. ; Hypergeometric functions of three variables. Ganita, 15(1964) , 97-108.
• [16] Srivastava, H. M. ; Some integrals representing triple hypergeometric functions. Rend. Circ. Mat. Palermo (Ser. 2), 16( 1967), 99-115.
• [17] Srivastava, H. M. and Manocha, H. L. ; A Treatise on Generating Functions Halsted Press (Ellis Horwood Limited, Chichester, U.K.) John Wiley and Sons, New york, Chichester, Brisbane and Toronto, 1984.
• [18] 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.
• [19] Slater,L.J. ; Generalized Hypergeometric Functions. Cambridge University Press, Cambridge, 1966.