Some Generating Relations of Extended Mittag-Leffler Funtions
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Motivated by the results on generating functions investigated by H. Exton and many other authors, we derive certain (presumably) new generating functions for generalized Mittag-Le er-type functions. Specifically, we introduce a new class of generating relations (which are partly bilateral and partly unilateral) involving the generalized Mittag-Le er function. Also we present some special cases of our main result.
Abstract
Motivated by the results on generating functions investigated by H. Exton and many other authors, we derive certain (presumably) new generating functions for generalized Mittag-Le er-type functions. Specifically, we introduce a new class of generating relations (which are partly bilateral and partly unilateral) involving the generalized Mittag-Le er function. Also we present some special cases of our main result.
참고문헌 (17)
- R. P. Agarwal, "A propos d'une note de M. pierre Humbert", C. R. Acad. Sci. Paris, 236, pp.2031~2032 (1953)
- A. Erdelyi, "Higher transcendental functions,Vol. I, (Bateman Manuscript Project)" (1953), McGraw-Hill, Book Co. Inc
- H. Exton, "A new generating function for the associated Laguerre polynomials and resulting expansions", Jnanabha, 13, pp.143~149 (1983)
- M. Kamarujjama, "Some generating relations involving Mittag-Leffler's function", Proc. International Conf., 2, pp.15~20 (2001), SSFA
- M. Kamarujjama, "On some generating relations involving generalized Mittag-Leffler's function", Southeast Asian Bull. Math, 36, pp.363~368 (2012)
- M. A. Khan, "On some properties of the generalized Mittag-Leffler function", Springer Plus, 2, pp.1~9 (2013)
- G. Mittag-Leffler, "Sur la representation analytique d'une branche uniforme d'une fonction monogene", Acta Math, 29, pp.101~181 (1905)
- M. A. Pathan, "On partly bilateral and partly unilateral generating functions", J. Aust. Math. Soc. Ser. B, 28, pp.240~245 (1986)
- T. R. Prabhakar, "A singular integral equation with a generalized Mittag-Leffler function in the kernel", Yokohama Math. J, 19, pp.7~15 (1971)
- R. K. Raina, "On generalised Wright's hypergeometric functions and fractional calculus operators", East Asian Math. J, 21(2), pp.191~203 (2005)
- E. D. Rainville, "Special functions" (1971), Chelsea Publ. Co.
- M. Saigo, "On Mittag-Leffler type function and applications", Integral Transform. Spec. Funct, 7, pp.97~112 (1998)
- T. O. Salim, "Some properties relating to the generalized Mittag-Leffler function", Adv. Appl. Math. Anal, 4, pp.21~30 (2009)
- T. O. Salim, "A generalization of Mittag-Leffler function and integral operator associated with fractional calculus", J. Fract. Cal. Appl, 3(5), pp.1~13 (2012)
- A. K. Shukla, "On a generalisation of Mittag-Leffler function and its properties", J. Math. Anal. Appl, 336, pp.797~811 (2007)
- H. M. Srivastava, "A treatise on generating functions" (1984), Halsted Press, John Wiley and Sons
- A.Wiman, "Uber den fundamentalsatz in der teorie der funktionen Eα(x)", Acta Math, 29, pp.191~201 (1905)
