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Surveys in Mathematics and its Applications ISSN 1842-6298 (electronic), 1843-7265 (print) Volume 4 (2009), 133 – 138 ON A RECURRENCE RELATION OF GENERALIZED MITTAG-LEFFLER FUNCTION Ajay K. Shukla and Jyotindra C. Prajapati Abstract. The principal aim of this paper is to investigate a recurrence relation and an integral representation of generalized Mittag-Leffler function Eγ,q α,β(z). In the end several special cases have also been discussed. Full text References [1] I. S. Gupta and L. Debnath, Some properties of the Mittag-Leffler functions, Integral Trans. Spec. Funct. No 18 (5) (2007), 329-336. MR2326071(2008f:33029). Zbl 1118.33011. [2] G. M. Mittag-Leffler, Sur la nouvelle fonction Eα (x), C. R. Acad. Sci. Paris No 137 (1903), 554-558. [3] T. R. Prabhakar, A singular integral equation with a generalized Mittag- Leffler function in the Kernel, Yokohama Math. J. No 19 (1971) 7-15. MR0293349(45#2426). Zbl 0221.45003. [4] E. D. Rainville, Special Functions,, The Macmillan Company, New York, 1960. MR0107725(21 #6447). Zbl 0092.06503. [5] A. K. Shukla and J. C. Prajapati, On a generalization of Mittag-Leffler function and its properties, J. Math. Anal. Appl. No 336 (2007), 797-811. MR2352981(2008m:33055). Zbl 1122.33017. [6] A. Wiman, Uber de fundamental satz in der theorie der funktionen Eα (x), Acta Math. No 29 (1905), 191-201. MR1555014. JFM 36.0471.01. 2000 Mathematics Subject Classification: Primary 33E12; Secondary 33B15. Keywords: Generalized Mittag-Leffler function; Recurrence relation; Wiman’s function. ****************************************************************************** 2 A. K. Shukla and J. C. Prajapati Ajay K. Shukla Jyotindra C. Prajapati Department of Mathematics, Department of Mathematics, S.V. National Institute of Technology, Faculty of Technology and Engineering, Surat-395 007, India. Charotar University of Science and Technology, e-mail: [email protected] Changa, Anand-388 421, India. e-mail: [email protected] ****************************************************************************** Surveys in Mathematics and its Applications 4 (2009), 132 – 138

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