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Here, in this paper, we aim at establishing some new unified integral and differential formulas associated with the $\overline{H}$-function. Each of these formula involves a product of the $\overline{H}$-function and Srivastava polynomials with essentially arbitrary coefficients and the results are obtained in terms of two variables $\overline{H}$-function. By assigning suitably special values to these coefficients, the main results can be reduced to the corresponding integral formulas involving the classical orthogonal polynomials including, for example, Hermite, Jacobi, Legendre and Laguerre polynomials. Furthermore, the $\overline{H}$-function occurring in each of main results can be reduced, under various special cases.
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참고문헌 (30)
참고문헌 신청
D. Baleanu / 2015 / Generalized fractional integration of the product of two H-functions and a general class of polynomials / Int. J. Comp. Math 2015:10
R. G. Buschman / 1990 / The H-function associated with a certain class of Feynman integrals / J. Phys. A. Math. Gen 23:4707~4710
J. Choi / 2014 / Certain unified fractional integrals and derivatives for a product of Aleph function and a general class of multivariable polynomials / J. Inequal. Appl 2014:15
A. Erdelyi / 1953 / Higher Transcenden-tal Function. Vol. I / Krieger
K. C. Gupta / 2006 / On a basic integral formula involving with the product of the H-function and Fox’s H-function / J. Raj. Acad. Phys. Sci 4(3):157~164
R. G. Buschman / 1990 / The H-function associated with a certain class of Feynman integrals / J. Phys. A. Math. Gen 23:4707~4710
J. Choi / 2014 / Certain unified fractional integrals and derivatives for a product of Aleph function and a general class of multivariable polynomials / J. Inequal. Appl 2014:15
A. Erdelyi / 1953 / Higher Transcenden-tal Function. Vol. I / Krieger
K. C. Gupta / 2006 / On a basic integral formula involving with the product of the H-function and Fox’s H-function / J. Raj. Acad. Phys. Sci 4(3):157~164
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