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A Study of Generalized Weyl Differintegral Operator Associated with a General Class of Polynomials and the Multivariable H-function

Ramesh Chandra Soni|Monica Wiseman
경북대학교 자연과학대학 수학과|2010.06|Kyungpook Mathematical Journal|제50권 제2호|pp. 229-235

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참고문헌

키워드

multivariable H-functiongeneral class of polynomialsDifferintegral operatorsH-function of FoxKonhauser biorthogonal polynomials
주제분류수학

초록

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.

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.

참고문헌 (17)

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  3. Konhauser J.D.E., "Biorthogonal polynomials suggested by the Laguerre polynomials", Pacific J. Math., 21, pp.303~314 (1967)
  4. Mathai A. M., "The H-function with applications in statistics and other disciplines" (1978), Wiley Eastern Limited
  5. Miller K.S., "An introduction to the fractional calculus and fractional differential equations" (1993), John Wiley and Sons
  6. Oldham K.B., "The fractional calculus" (1974), Academic Press
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  8. Saigo M., "A certain boundary value problem for the Euler-Darboux equation Ⅰ, Ⅱ and Ⅲ", Math. Japon., 24, pp.377~385 (1979)
  9. Saigo M., "Fractional calculus operators associated with a general class of polynomials", Fukuoka Univ. Sci. Rep., 18, pp.15~22 (1988)
  10. Saigo M., "Fractional calculus operators associated with the H-function of several variables. in: Analysis, Geometry and Groups: A Riemann Legacy Volume", pp.527~538 (1993), Hadronic Press
  11. Srivastava H. M., "A contour integral involving Fox's H-function", Indian J. Math., 14, pp.1~6 (1972)
  12. Srivastava H. M., "Some biorthogonal polynomials suggested by the Laguerre polyno-mials", Pacific J. Math., 98, pp.235~250 (1982)
  13. Srivastava H. M., "The Weyl fractional integral of a general class of polynomials", Boll. Un. Mat. Ital., 2-B, pp.219~228 (1983)
  14. Srivastava H. M., "The H-functions of one and two variables with applications" (1982), South Asian Publishers
  15. Srivastava H. M., "Some bilateral generating functions for a class of generalized hypergeometric polynomials", J. Reine Angew. Math., 283, pp.265~274 (1976)
  16. Srivastava H. M., "Multiplication of fractional calculus operators and boundary value problems involving the Euler-Darboux equation", J. Math. Anal. Appl., 121, pp.325~369 (1987)
  17. Srivastava H. M., "The integration of certain products of the multi-variable H-function with a general class of polynomials", Rend. Circ. Mat. Palermo, 32, pp.157~187 (1983)

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