DOI QR코드

DOI QR Code

SOME INTEGRALS ASSOCIATED WITH MULTIINDEX MITTAG-LEFFLER FUNCTIONS

  • KHAN, N.U. ;
  • USMAN, T. ;
  • GHAYASUDDIN, M.
  • Received : 2015.07.28
  • Accepted : 2015.10.21
  • Published : 2016.05.30

Abstract

The object of the present paper is to establish two interesting unified integral formulas involving Multiple (multiindex) Mittag-Leffler functions, which is expressed in terms of Wright hypergeometric function. Some deduction from these results are also considered.

Keywords

Multiple (multiindex) Mittag-Leffler Function;Wright Hypergeometric Function and Integrals

References

  1. C. Fox, The asymptotic expansion of generalized hypergeometric functions, Proc. London Math. Soc. S2-27 (1928), 389-400. https://doi.org/10.1112/plms/s2-27.1.389
  2. J. Choi, A. Hasnove, H.M. Srivastava and M. Turaev, Integral representations for Srivastava’s triple hypergeometric functions, Taiwanese J. Math. 15 (2011), 2751-2762. https://doi.org/10.11650/twjm/1500406495
  3. J. Choi, P. Agarwal, S. Mathur and S.D. Purohit, Certain new integral formulas involving the generalized Bessel functions, Bull. Korean Math. Soc. 51 (2014), 995-1003. https://doi.org/10.4134/BKMS.2014.51.4.995
  4. J. Choi and P. Agarwal, Certain unified integrals involving a product of Bessel functions of first kind, Honam Mathematical J. 35 (2013), 667-677. https://doi.org/10.5831/HMJ.2013.35.4.667
  5. J. Choi and P. Agarwal, Certain Unified Integrals Associated with Bessel Functions, Boundary Value Problems, 2013 (2013:95), 9 pp. . https://doi.org/10.1186/1687-2770-2013-9
  6. F. Oberhettinger, Tables of Mellin Transforms, Springer, New York, 1974.
  7. P. Agarwal, S. Jain, S. Agarwal and M. Nagpal, On a new class of integrals involving Bessel functions of the first kind, Communication in Numerical Analysis, 2014 (2014), 1-7. https://doi.org/10.5899/2014/cna-00216
  8. E.D. Rainville, Special functions, The Macmillan Company, New York, 2013.
  9. H.M. Srivastava and H.L. Manocha, A Treatise on generating functions, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and sons, New York, 1984.
  10. H.M. Srivastava and P.W. Karlsson, Multiple Gaussian Hypergeometric Series, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane, and Toronto, 1985.
  11. Virgina S. Kiryakova, Multiple (multiindex) Mittag-Leffler functions and relations to generalized fractional calculus, J. Comput. Appl. Math.,118 (2000) 241-259. https://doi.org/10.1016/S0377-0427(00)00292-2
  12. E.M. Wright, The asymptotic expansion of the generalized hypergeometric functions, J. London Math. Soc. 10 (1935), 286-293.
  13. E.M. Wright, The asymptotic expansion of integral functions defined by Taylor series, Philos. Trans. Roy. Soc. London, A238, (1940), 423-451. https://doi.org/10.1098/rsta.1940.0002
  14. E.M. Wright, The asymptotic expansion of the generalized hypergeometric function II, Proc. Lond. Math. Soc. S2-46 (1940), 389-408. https://doi.org/10.1112/plms/s2-46.1.389
  15. Y.A. Brychkov, Handbook of Special Functions, Derivatives, Integrals, Series and Other Formulas, CRC Press, Taylor and Francis Group, Boca Raton, London, and New York, 2008.