Kyungpook Mathematical Journal

  • 제48권2호
  • /
  • Pages.165-171
  • /
  • 2008
  • /
  • 1225-6951(pISSN)
  • /
  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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Some Finite Integrals Involving The Product of Srivastava's Polynomials and A Certain $\bar{H}$-Function with Applications

  • Singh, Yashwant (Department of Mathematics, S.M.L.(P.G.)College) ;
  • Garg, Atul (Department of Mathematics, S.M.L.(P.G.)College)
  • 투고 : 2003.09.15
  • 발행 : 2008.06.30
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초록

The aim of this paper is to evaluate four finite integrals involving the product of Srivastava's polynomials, a generalized hypergeometric function and $\bar{H}$-function proposed by Inayat Hussian which contains a certain class of Feynman integrals. At the end, we give an application of our main findings by connecting them with the Riemann-Liouville type of fractional integral operator. The results obtained by us are basic in nature and are likely to find useful applications in several fields notably electric networks, probability theory and statistical mechanics.

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참고문헌

  1. R.G. Buschman and H.M. Srivastava, The H-function associated with a certain class of Feynman integrals, J.Phys. A: Math. Gen., 23 (1990), 4707-4710. https://doi.org/10.1088/0305-4470/23/20/030
  2. A. et.al. Erdelyi, Tables of Integral Transforms, vol.II, McGraw-Hill, New-York (1954).
  3. K.C. Gupta and R.C. Soni, New properties of a generalization of hypergeometric series associated with feynman integrals,Kyungpook Mathematical Journal, vol.4(1), (2001), 97-104.
  4. A.A. Inayat-Hussian, New properties of hypergeometric series deriable from feynman integrals:I; Transformation and reduction formulae, J.Phys. A:Math.Gen. 20 (1987), 4109-4117. https://doi.org/10.1088/0305-4470/20/13/019
  5. A.A. Inayat-Hussian, New properties of hypergeometric series deriable from feynman integrals:II; A generalization of the H-function, J.Phys. A:Math.Gen. 20 (1987), 4119-4128. https://doi.org/10.1088/0305-4470/20/13/020
  6. E.D. Rainville, Special Functions, The Macmillan Company Inc., NewYork (1963).
  7. H.M. Srivastava, A contour integral involving Fox's H-function, Indian J.Math., 14 (1972), 1-6.
  8. H.M. Srivastava, K.C. Gupta and S.P. Goyal, The H-function of One and Two Variables with Application; South Asian Publisher, New Delhi (1982).
  9. H.M. Srivastava and N.P. Singh, The integration of certain products of the multivariable H-function with a general class of polynomials, Rend. Circ. Math.Palermo, (Ser2), 32 (1983), 157-187. https://doi.org/10.1007/BF02844828