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Certain integral formulas associated with Aleph (ℵ)-function

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Recently many authors have investigated so-called Aleph $(\aleph)$-function and its various properties. Here, in this paper, we aim at establishing certain integral formulas involving the Aleph $(\aleph)$-function. Precisely, integrals with product of Aleph $(\aleph)$-function with Jacobi polynomials, Bessel Maitland function, general class of polynomials were under consideration. Some interesting special cases of our main result are also considered and shown to be connected with certain known ones.

Abstract

Recently many authors have investigated so-called Aleph $(\aleph)$-function and its various properties. Here, in this paper, we aim at establishing certain integral formulas involving the Aleph $(\aleph)$-function. Precisely, integrals with product of Aleph $(\aleph)$-function with Jacobi polynomials, Bessel Maitland function, general class of polynomials were under consideration. Some interesting special cases of our main result are also considered and shown to be connected with certain known ones.

참고문헌 (15)

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  2. Y. Khan, "Some integral properties of Aleph function, general class of polynomials associated with Feynman integrals", IJMSI, 2(1), pp.21~27 (2014)
  3. 2A. Erd´elyi, "Higher Transcendental Functions. Vol. I, II" (1953), McGraw-Hill
  4. V. S. Kiryakova, "Generalized fractional calculus and applications, Pitamat Research Notes in Mathematics", pp.301~ (1994), Johan Wiley and Sones
  5. A. A. Kilbas, "Theory and Applications of Fractional Differential Equations, North-Holland Mathematical Studies, Vol. 204" (2006), Elsevier (North-Holland) Science Publishers
  6. A. M. Mathai, "The H-function with Applications in Statistics and Other Disciplines" (1978), Halsted Press (John Wiley & Sons)
  7. A. M. Mathai, "The H-Function: Theory and Appli-cations" (2010), Springer
  8. E. D. Rainville, "Special Function" (1960), The Macmillan Company
  9. R. K. Saxena, "Mathieu-type series for the @-function occurring in Fokker-Planck equation", Eur. J. Pure Appl. Math, 3(6), pp.980~988 (2010)
  10. R. K. Saxena, "On fractional integral fromulae for @-function", Appl. Math. Comput, 218, pp.985~990 (2011)
  11. V. P. Saxena, "Formal solution of certain new pair of dual integral equations involving H-function", Proc. Nat. Acad. Sci. India Sect, A51, pp.366~375 (2001)
  12. H. M. Srivastava, "A multilinear generating function for the Konhauser sets of biorthog-onal polynomials suggested by the Laguerre polynomials", Pacific J. Mat, 117(1), pp.183~191 (1985)
  13. H. M. Srivastava, "The integration of certain of product multivariable H-function with a general class of polynomials", Rend. Circ. Mat. Palermo Ser, 32(2), pp.157~187 (1983)
  14. N. S¨udland, "Open problem: Who knows about the ℵ-function?", Appl. Anal, 1(4), pp.401~402 (1998)
  15. N. S¨udland, "Computer Algebra in Scientific Computing", pp.513~525 (2001), Springer

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