Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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New Properties of a Generalization of Hypergeometric Series Associated with Feynman Integrals

K. C. GUPTA

  • Published : 20010000

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Abstract

In the present paper we study the H-function proposed by Inayat-Hussain which contain a certain class of Feynman Integrals, the exact partition function of the Gaussian model in statistical mechanics and several other functions as its particular cases. During the course of study, we evaluate a new finite integral involving this function and product of two general class of polynomials. This integral is unified in nature and acts as a key formula from which we can derive as its particular cases, integrals involving a large number of simpler special functions and polynomials. For the sake of illustration, we give here only two particular cases of our main integral which are also new and of interest by themselves. At the end. We give applications of our main findings by interconnecting 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 electrical networks, probability theory and statistical mechanics.

Keywords

References

  1. Compositio Math. v.15 Asymptotic expansisons and analytic continuations for a class of Bernes-integrals Braaksma B. L. J.
  2. J. Phys. A. : Math. Gen. v.23 The H-function associated with a certain class of Feynman integrals Buschman R. G.;Srivastava H. M.
  3. Tables of integral transforms v.2 Erdelyi A.;Magnus W.;Oberhettinger F.;Tricomi F. G.
  4. Trans. Amer. Math. Soc. v.98 The G and H functions as symmetrical Fourier kernels Fox C.
  5. Proc. Nat. Acad. Sci. India Sect. v.39 no.A A finite integral involving H-function Goyal G. K.
  6. Springer tracts in modern physics v.145 Handbook of Feynman path integrals Grosche C.;Steiner F.
  7. The double Mellin-Barnes type integrals and their applications to convolution theory Hai N. T.;Yakubovich S. B.
  8. J. Phys. A : Math. Gen. v.20 New properties of hypergeometric series derivable from Feynman integrals : I. Transformation and reduction formulae Inayat-Hussian A. A.
  9. J. Phys. A : Math. Gen. v.20 New properties of hypergeometric series derivable from Feynman integrals : II. A generalization of the H function Inayat-Hussian A. A.
  10. The H-function with applications in statistics and other disciplines Mathai A. M.;Saxena, R. K.
  11. The fractional calculus Oldham K. B.;Spanier J.
  12. Le Matematiche Fasc. II. v.52 A new generalization of generalized hypergeometric functions Rathie A. K.
  13. Indian J. Math. v.14 A contour integral involving Fox's H-function Srivastava H. M.
  14. The H-functions of one and two variables with applications Srivastava H. M.;Gupta K. C.;Goyal S. P.
  15. Rend. Circ. Mat. Palermo v.32 The integration of certain products of the multivariable H-function with a general class of polynomials Srivastava H. M.;Singh N. P.