Let sand zbe complex variables, Γ(s)be the Gamma function, and for any complex v be the generalized Pochhammer symbol. Wright Type Hypergeometric Function is defined(Virchenko et al. ), as: where which is a direct generalization of classical Gauss Hypergeometric Function2F1(a,b;c;z). The principal aim of this paper is to study the various properties of this Wright type hypergeometric function2R1(a,b;c;τ;z);which includes differentiation and integration, representation in terms ofpFq and in terms of Mellin-Barnes type integral. Euler (Beta) transforms, Laplace transform, Mellin transform,Whittaker transform have also been obtained; along with its relationship with Fox H-function and Wright hypergeometric function.
Cite this paper
S. Rao, J. Prajapati and A. Shukla, "Wright Type Hypergeometric Function and Its Properties," Advances in Pure Mathematics, Vol. 3 No. 3, 2013, pp. 335-342. doi: 10.4236/apm.2013.33048.
 N. Virchenko, S. L. Kalla and A. Al-Zamel, “Some Results on a Generalized Hypergeometric Function,” Integral Transforms and Special Functions, Vol. 12, No. 1, 2001, pp. 89-100. doi:10.1080/10652460108819336
 E. D. Rainville, “Special Functions,” The Macmillan Company, New York, 1960.
 A. Erdelyi, et al., “Higher Transcendental Functions,” McGaw-Hill, New York, 1953-1954.
 E. M. Wright, “On the Coefficient of Power Series Having Exponential Singularities,” Journal London Mathematical Society, Vol. s1-8, No. 1, 1933, pp. 71-79.
 M. Dotsenko, “On Some Applications of Wright’s Hypergeometric Function,” Comptes Rendus de l’Académie Bulgare des Sciences, Vol. 44, 1991, pp. 13-16.
 V. Malovichko, “On a Generalized Hypergeometric Function and Some Integral Operators,” Mathematical Physics, Vol. 19, 1976, pp. 99-103.
 L. Galue, A. Al-Zamel and S. L. Kalla, “Further Results on Generalized Hypergeometric Functions,” Applied Mathematics and Computation, Vol. 136, No. 1, 2003, pp. 17-25. doi:10.1016/S0096-3003(02)00014-0
 I. N. Sneddon, “The Use of Integral Transforms,” Tata McGraw-Hill Publication Co. Ltd., New Delhi, 1979.
 H. M. Srivastava and H. L. Manocha, “A Treatise on Generating Functions,” John Wiley and Sons/Ellis Horwood, New York/Chichester, 1984.
 A. M. Mathai, R. K. Saxena and H. J. Haubold, “The H-Function,” Springer, Berlin, 2010.