Note on the pRq(α; β; z) Function


Affiliations

  • K. J. Somaiya College of Engineering, Somaiya Vidyavihar University, Department of Science and Humanities, Mumbai, 400077, India
  • S.V. National Institute of Technology, Department of Applied Mathematics and Humanities, Surat, 395007, India

Abstract

The aim of this paper is to give some convergence conditions of the pRq(α; β; z) function. We also derive the integral representation of the function pRq(α; β; z) in the form of Mellin-Barnes Integral including its analytic property.

Keywords

Mellin{Barnes Integral, Mittag{Leer function, hypergeometric function, Wright functions

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References

G. E. Andrew, R. Askey and R. Roy, Special Functions (Encyclopedia of Mathematics and its Applications), Cambridge University Press, UK, 1999.

H. Bateman, Higher Transcendental Functions Vol. 3, McGraw-Hill, New York 1955.

R. Desai and A. K. Shukla, Some results on function pRq(α; β; z), J. Math. Anal. Appl., 448(1)(2017), 187-197.

C. Fox, The G and H functions as symmetrical Fourier kernels, Trans. Amer. Math. Soc. 98(3)(1961), 395-429.

R. Goren o, A. A. Kilbas, F. Mainardi and S. V. Rogosin, Mittag-Leffler Functions, Related Topics and Applications, Springer, Berlin, 2014.

A. A. Kilbas, M. Saigo and J. J. Trujillo,On the generalized Wright function, Fract. Calc. Appl. Anal.,5(4)(2002), 437-460.

A. M. Mathai and H. J. Haubold, Special Functions for Applied Scientists, Springer, New York, 2008.

K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Di erential Equations, John Wiley and Sons, New York, 1993.

G. M. Mittag{Leer, Sur la nouvelle fonction E (x), CR Acad Sci Paris, 137(1903), 554-558.

E. D. Rainville, Special Functions, Mcmillan, New York, 1960.

T. O. Salim, Some properties relating to the generalized Mittag-Leer function, Adv. Appl. Math. Anal., 4(1)(2009), 21-30.

M. Shahed and A. Salem, An Extension of Wright function and its properties, J. Math., 2015, (2015)

M. Sharma and R. Jain, A note on a generalized M-series as a special function of fractional calculus, Fract. Calc. Appl. Anal. 12(4)(2009), 449-452.

G. N. Watson, A Treatise on The Theory of Bessel Functions, Cambridge University Press, Cambridge, 1995.

E. M. Wright, On the coecient of power series having exponential singularities, J. London Math. Soc. 5(1933), 71-79.


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