Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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On Certain Integral Transforms Involving Hypergeometric Functions and Struve Function

  • Singhal, Vijay Kumar (Department of Mathematics, Swami Keshvanand Institute of Technology, Management and Gramothan) ;
  • Mukherjee, Rohit (Department of Mathematics, Swami Keshvanand Institute of Technology, Management and Gramothan)
  • Received : 2016.01.05
  • Accepted : 2016.07.06
  • Published : 2016.12.23
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Abstract

This paper is devoted to the study of Mellin, Laplace, Euler and Whittaker transforms involving Struve function, generalized Wright function and Fox's H-function. The main results are presented in the form of four theorems. On account of the general nature of the functions involved here in, the main results obtained here yield a large number of known and new results in terms of simpler functions as their special cases. For the sake of illustration some corollaries have been recorded here as special cases of our main findings.

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References

  1. B. L. G. Braaksma, Asymptotic expansions and analytic continuation for a class of Barnes Integrals, Compositio Math., 15(1964), 239-341.
  2. M. M. Dzherbashyan, Integral Transforms and Representations of Functions in the Complex Domain, Nauka, Moscow, 1966(in Russian).
  3. A. Erdelyi (Ed.) et al., Higher Transcendental Functions, Vols. 1-3, McGraw-Hill, New York(1953).
  4. I. S. Gradshteyin and IM. Ryzhik, Table of Integrals, series and products, 6/e, Academic press, New Delhi(2001).
  5. A. Kilbas and M. Saigo, and J. Trujillo, On the generalized Wright function, Fract. Calc. Appl. Anal., 5(4)(2002), 437-460.
  6. E. Kratzel, Integral transformationsof Bessel type, Generalized functions and Operational calculus, Proc. Conf. Verna, 1975, Bulg. Acad. Sci., Sofia(1979), 148-165.
  7. O. I. Marichev, Handbook of Integral Transforms of Higher Transcendental Functions:Theory and Algorithmic Tables Ellis Horwood and Halsted Press, New York(1983).
  8. A. M. Mathai and H. J. Haubold, Special Functions for Applied Scientists, Springer(2008).
  9. A. M. Mathai and R. K. Saxena, The H-function with Applications in Statistics and Other Disciplines, Wiley East. Ltd., New Delhi(1978).
  10. T. G. Pederson, Variational approach to excitons in carbon nanotubes, Phys. Rev. B, 67(7)(2003), 1-4.
  11. I. Podlubny, Fractional Differential Equations, Acad. Press, San Diego(1999).
  12. A. Prudnikov, Yu. Brychkov and O. Marichev, Integrals and Series, Some More Special Functions, vol. 3, Gordon and Breach, New York(1992).
  13. O. Salim Tariq and W. Faraj Ahmed, A generalization of Mittag-Leffler function and integral operator associated with Fractional calculus, J. Fract. Cal. Appl., Vol.3(2012) No.5, 1-13. https://doi.org/10.1142/9789814355216_0001
  14. J. Shao and P. Hanggi, Decoherent dynamics of a two level system coupled to a sea of spins, Phys. Rev. Lett., 81(26)(1988), 5710-5713. https://doi.org/10.1103/PhysRevLett.81.5710
  15. A. K. Shukla and J. C. Prajapati, On a generalization of Mittag-Leffler function and its properties, J. Math. Anal. Appl., 336(2007), 797-811. https://doi.org/10.1016/j.jmaa.2007.03.018
  16. I. N. Sneddon, The use of Integral Transforms, New Delhi: TMH;1979
  17. H. M. Srivastava, A contour integral involving Fox's H-function, Indian J. Math., 14(1972), 1-6.
  18. H. M. Srivastava, K. C. Gupta and S. P. Goyal, The H-Functions of One and Two Variables with Applications, South Asian Publs., New Delhi(1982).
  19. H. M. Srivastava and B. R. K. Kashyap, Special Functions in Queuing Theory and Related Stochastic Processes, Acad. Press, New York(1981).
  20. H. M. Srivastava and Z. Tomovski, Fractional calculus with an integral operator containing a generalized Mittag-Leffler function in the kernel, Appl. Math. Comput., Vol.211(2009), 198-210.
  21. H. Struve, Beitrag zur Theorie der Diffraction an Fernrohren, Ann. Physik Chemie, 17(1882), 1008-1016.
  22. G. N. Watson, A treatise on the theory of Bessel functions, 2nd ed., Cambridge univ. press, London 1966.
  23. A. Wiman, Uber den fundamental satz in der theory der funcionen, Acta Math., Vol.29(1905),191-201. https://doi.org/10.1007/BF02403202
  24. E. M. Wright, The asymptotic expansion of the generalized hypergeometric Function, London Math. Soc., 10(1935), 257-260.