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Euler type integral involving generalized Mittag-Leffler function

Shakeel Ahmed|Mumtaz Ahmad Khan
대한수학회 (The Korean Mathematical Society)|2014.07|대한수학회논문집 (Communications of the KMS)|제29권 제3호|pp. 479-487

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참고문헌

키워드

Mittag-Leffler functionextended beta functionEuler type integralsWiman functionPrabhakar function
주제분류수학

초록

In this paper, we obtain some theorems on certain Euler type integrals involving generalized Mittag-Leffler function. Further, we deduce some special cases involving Wiman function, Prabhakar function and exponential and binomial functions.

Abstract

In this paper, we obtain some theorems on certain Euler type integrals involving generalized Mittag-Leffler function. Further, we deduce some special cases involving Wiman function, Prabhakar function and exponential and binomial functions.

참고문헌 (11)

  1. L. C. Andrews, "Special Functions of Mathematics for Engineers" (1998), Oxford University Press
  2. L. Carlitz, "Some extension and convolution formulas related to Mac Mohan’s master theorems", SIAM J. Math. Anal, 8(2), pp.320~336 (1977)
  3. M. A. Chaudhry, "Extension of Euler’s beta function", J. Comput. Appl. Math, 78(1), pp.19~32 (1997)
  4. M. A. Chaudhry, "Generalized incomplete gamma functions with applications", J. Comput. Appl. Math, 55(1), pp.99~124 (1994)
  5. S. Khan, "Evaluations of certain Euler type integrals", Appl. Math. Comput, 189(2), pp.1993~2003 (2007)
  6. G. M. Mittag-Leffler, "Sur la nouvelle fonction Eα(x)", C. R. Acad. Sci. Paris, 137, pp.554~558 (1903)
  7. T. R. Prabhakar, "A singular integral equation with a generalized Mittag Leffler function in the kernel", Yokohama Math. J, 19, pp.7~15 (1971)
  8. A. P. Prudnikov, "Integrals and Series, vol. 1" (1990), Gordan and Breach Science Publishers
  9. E. D. Rainville, "Special Functions" (1960), Macmillan
  10. A. K. Shukla, "On a generalization of Mittag-Leffler function and its properties", J. Math. Anal. Appl, 336(2), pp.797~811 (2007)
  11. A. Wiman, "Uber den Fundamental Satz in der Theorie der Funktionen Eα(x)", Acta Math, 29(1), pp.191~201 (1905)

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