Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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ON A RECURRENCE RELATION OF K-MITTAG-LEFFLER FUNCTION

  • Received : 2012.07.13
  • Published : 2013.10.31
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Abstract

The principal aim of this paper is to investigate a recurrence relation and an integral representation of k-Mittag-Leffler function introduced earlier by Dorrego and Cerutti [2] and several special cases have also been discussed.

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References

  1. R. P. Agrawal, A propos d'une Note M. Pierre Humbert, C. R. Math. Acad. Sc. Paris 236 (1953), 2031-2032.
  2. G. A. Dorrego and R. A. Cerutti, The k-Mittag-Leffler function, Int. J. Contemp. Math. Sciences 7 (2012), no. 15, 705-716.
  3. M. M. Dzrbasjan, On the integral representation and uniqueness of some classes of entire functions, Mat. Sb. (N.S.) 33(75) (1953), no. 3, 485-530.
  4. M. M. Dzrbasjan, On the integral transformations generated by the generalized Mittag-Leffler functions, Izv. AN Arm. SSR 13 (1960), no. 3, 21-63.
  5. M. M. Dzrbasjan, Integral Transforms and Representations of Functions in the Complex Domain, Nauka, Moscow, 1966.
  6. R. Gorenflo, A. A. Kilbas, and S. V. Rosogin, On the generalized Mittag-Leffler type functions, Integral Transform. Spec. Funct. 7 (1998), no. 3-4, 215-224. https://doi.org/10.1080/10652469808819200
  7. I. S. Gupta and L. Debuath, Some properties of the Mittag-Leffler functions, Integral Transforms Spec. Funct. 18 (2007), no. 5-6, 329-336. https://doi.org/10.1080/10652460601090216
  8. P. Humbert and R. P. Agrawal, Sur la fonction de Mittag-Leffler et quelques-unes de ses generalisations, Bull. Sci. Math. (2) 77 (1953), 180-185.
  9. G. M. Mittag-Leffler, Sur la nuovelle function Ea(x), C. R. Acad. Sci. Paris (2) 137 (1903), 554-558.
  10. G. M. Mittag-Leffler, Sur la representation analytique d'une branche uniforme d'une fonction monogene, Acta Math. 29 (1905), no. 1, 101-181. https://doi.org/10.1007/BF02403200
  11. T. R. Prabhakar, A singular integral equation with a generalized Mittag-Leffler functions in the Kernel, Yokohama Math. J. 19 (1971), 7-15.
  12. A. K. Shukla and J. C. Prajapati, On a generalization of Mittag-Leffler function and its properties, J. Math. Anal. Appl. 336 (2007), no. 2, 797-811. https://doi.org/10.1016/j.jmaa.2007.03.018
  13. A. Wiman, Uber die Nullsteliun der Fuctionen Ea(x), Acta Math. 29 (1905), 217-234. https://doi.org/10.1007/BF02403204