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A NOTE ON CERTAIN LAPLACE TRANSFORMS FOR THE GENERALIZED HYPERGEOMETRIC FUNCTION 3F3

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초록

The main objective of this paper is to demonstrate how one can obtain very quickly so far unknown Laplace transforms of rather general cases of the generalized hypergeometric function 3F3 by employing generalizations of classical summation theorems for the series 3F2 available in the literature. Several new as well known results obtained earlier by Kim et al. follow special cases of main findings.

Abstract

The main objective of this paper is to demonstrate how one can obtain very quickly so far unknown Laplace transforms of rather general cases of the generalized hypergeometric function 3F3 by employing generalizations of classical summation theorems for the series 3F2 available in the literature. Several new as well known results obtained earlier by Kim et al. follow special cases of main findings.

참고문헌 (13)

  1. W.N. Bailey, "Generalized Hypergeometric Series" (1964), Cambridge University Press;Stechert-Hafner
  2. J. Choi, "On several new general Laplace transforms for generalized hypergeometric functions <TEX>$_1F_1$<", TEX>(a; b; x), 2016
  3. B. Davis, "Integral Transforms and Their Applications" (2002), Springer
  4. G. Doetsch, "Introduction to the theory and application of Laplace transformations" (1974), Springer
  5. A. Erdelyi, "Tables of Integral Trans-forms. Vol. I and II" (1954), McGraw Hills
  6. Y.S. Kim, "New Laplace transforms of Kummer's conuent hypergeometric functions", Math. Comp. Modelling, 50, pp.1068~1071 (2002)
  7. 김용섭, "New Laplace transforms for the generalized hypergeometric function $_2F_2$", 호남수학학술지, 37(2), pp.245~252 (2015), 호남수학회
  8. J.L. Lavoie, "Generalizations of Watson's theorem on the sum of a <TEX>$_3F_2$<", TEX>, 1992, pp.34, 23~32
  9. J.L. Lavoie, "Generalizations of Dixon's theorem on the sum of a <TEX>$_3F_2$<", TEX>, 1994, pp.62, 267~276
  10. J.L. Lavoie, "Generalizations of Whipple's theorem on the sum of a <TEX>$_3F_2$<", TEX>, 1996, pp.72, 293~300
  11. E.D. Rainville, "Special Functions" (1971), Chelsea Publishing Company, Brox
  12. L.J. Slater, "Generalized Hypergeometric Functions" (1966), Cambridge University Press
  13. H.M. Srivastava, "Zeta and q-zeta Functions and Associated Series and Integrals" (2012), Elsevier Science Publishers

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