Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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A Study of Generalized Weyl Differintegral Operator Associated with a General Class of Polynomials and the Multivariable H-function

  • Received : 2006.06.10
  • Accepted : 2008.05.29
  • Published : 2010.06.30
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Abstract

In the present paper, we obtain a new formula for the generalized Weyl differintegral operator in a compact form avoiding the occurrence of infinite series and thus making it useful in applications. Our findings provide interesting generalizations and unifications of the results given by several authors and lying scattered in the literature.

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References

  1. Banerji P.K. and Choudhary Sudipto, Fractional integral formulae involving general class of polynomials, Proc. Nat. Acad. Sci. India, 66(1996), 271-277.
  2. Fox C., The G and H-functions as symmetrical Fourier kernels, Trans. Amer. Math.Soc., 98(1961), 395-429.
  3. Konhauser J.D.E., Biorthogonal polynomials suggested by the Laguerre polynomials, Pacific J. Math., 21(1967), 303-314. https://doi.org/10.2140/pjm.1967.21.303
  4. Mathai A. M. and Saxena R.K., The H-function with applications in statistics and other disciplines, Wiley Eastern Limited, New Delhi, 1978.
  5. Miller K.S. and Ross B., An introduction to the fractional calculus and fractional differential equations, John Wiley and Sons, New York, 1993.
  6. Oldham K.B. and Spanier J., The fractional calculus, Academic Press, New York, 1974.
  7. Saigo M., A remark on integral operators involving the Gauss hypergeometric func- tions, Math. Rep. Kyushu Univ., 11(1978), 135-143.
  8. Saigo M., A certain boundary value problem for the Euler-Darboux equation I, II and III, Math. Japon., 24(1979), 377-385.
  9. Saigo M., A certain boundary value problem for the Euler-Darboux equation I, II and III, Math. Japon., 25(1980), 211-220.
  10. Saigo M., A certain boundary value problem for the Euler-Darboux equation I, II and III, Math. Japon., 26(1981), 103-119.
  11. Saigo M. and Raina R.K., Fractional calculus operators associated with a general class of polynomials, Fukuoka Univ. Sci. Rep., 18(1988), 15-22.
  12. Saigo M. and Raina R.K., Fractional calculus operators associated with the H-function of several variables, (H.M. Srivastava and Th. M. Rassias, Editors) Analysis, Geometry and Groups: A Riemann Legacy Volume, Hadronic Press, Palm Harbor, Florida 34682-1577, U.S.A. ISBN 0-911767-59-2 (1993), 527-538.
  13. Srivastava H. M., A contour integral involving Fox's H-function, Indian J. Math., 14(1972), 1-6.
  14. Srivastava H. M., Some biorthogonal polynomials suggested by the Laguerre polyno- mials, Pacific J. Math., 98(1982), 235-250. https://doi.org/10.2140/pjm.1982.98.235
  15. Srivastava H. M., The Weyl fractional integral of a general class of polynomials, Boll. Un. Mat. Ital., 2-B(1983), 219-228.
  16. Srivastava H. M., Gupta K.C. and Goyal S.P., The H-functions of one and two variables with applications, South Asian Publishers, New Delhi, 1982.
  17. Srivastava H. M. and Panda R., Some bilateral generating functions for a class of generalized hypergeometric polynomials, J. Reine Angew. Math., 283/284(1976), 265- 274.
  18. Srivastava H. M. and Saigo M., Multiplication of fractional calculus operators and boundary value problems involving the Euler-Darboux equation, J. Math. Anal. Appl., 121(1987), 325-369. https://doi.org/10.1016/0022-247X(87)90251-4
  19. Srivastava H. M. and Singh N.P., The integration of certain products of the multi- variable H-function with a general class of polynomials, Rend. Circ. Mat. Palermo, 32(1983), 157-187. https://doi.org/10.1007/BF02844828