APM  Vol.3 No.3 , May 2013
Wright Type Hypergeometric Function and Its Properties
ABSTRACT

Let s and z be 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. [1]), as: where which is a direct generalization of classical Gauss Hypergeometric Function 2F1(a,b;c;z). The principal aim of this paper is to study the various properties of this Wright type hypergeometric function 2R1(a,b;c;τ;z); which includes differentiation and integration, representation in terms of pFq 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.
References
[1]   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

[2]   E. D. Rainville, “Special Functions,” The Macmillan Company, New York, 1960.

[3]   A. Erdelyi, et al., “Higher Transcendental Functions,” McGaw-Hill, New York, 1953-1954.

[4]   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. doi:10.1112/jlms/s1-8.1.71

[5]   M. Dotsenko, “On Some Applications of Wright’s Hypergeometric Function,” Comptes Rendus de l’Académie Bulgare des Sciences, Vol. 44, 1991, pp. 13-16.

[6]   V. Malovichko, “On a Generalized Hypergeometric Function and Some Integral Operators,” Mathematical Physics, Vol. 19, 1976, pp. 99-103.

[7]   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

[8]   I. N. Sneddon, “The Use of Integral Transforms,” Tata McGraw-Hill Publication Co. Ltd., New Delhi, 1979.

[9]   H. M. Srivastava and H. L. Manocha, “A Treatise on Generating Functions,” John Wiley and Sons/Ellis Horwood, New York/Chichester, 1984.

[10]   A. M. Mathai, R. K. Saxena and H. J. Haubold, “The H-Function,” Springer, Berlin, 2010. doi:10.1007/978-1-4419-0916-9

 
 
Top