Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
Volume 4 (2009), 133 -- 138


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 Eα ,β γ ,q (z). In the end several special cases have also been discussed.

2000 Mathematics Subject Classification: Primary 33E12; Secondary 33B15.
Keywords: Generalized Mittag-Leffler function; Recurrence relation; Wiman's function.

Full text


  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.

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: Changa, Anand-388 421, India.