대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제31권2호
  • /
  • Pages.329-342
  • /
  • 2016
  • /
  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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NEW CLASS OF INTEGRALS INVOLVING GENERALIZED HYPERGEOMETRIC FUNCTION AND THE LOGARITHMIC FUNCTION

  • Kim, Yongsup (Department of Mathematics Education Wonkwang University)
  • 투고 : 2015.07.06
  • 발행 : 2016.04.30
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초록

Motivated essentially by Brychkov's work [1], we evaluate some new integrals involving hypergeometric function and the logarithmic function (including those obtained by Brychkov[1], Choi and Rathie [3]), which are expressed explicitly in terms of Gamma, Psi and Hurwitz zeta functions suitable for numerical computations.

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참고문헌

  1. Y. A. Brychkov, Evaluation of some classes of definite and indefinite integrals, Integral Transforms Spec. Funct. 13 (2002), no. 2, 163-167. https://doi.org/10.1080/10652460212896
  2. Y. A. Brychkov, Handbook of Special Functions, Derivatives, Integrals, Series and Other Formulas, CRC Press, Taylor & Francis Group: Boca Raton, London, New York, 2008.
  3. J. Choi and A. K. Rathie, Evaluation of certain new class of definite integrals, Integral Transforms Spec. Funct. 26 (2015), no. 4, 282-294. https://doi.org/10.1080/10652469.2014.1001385
  4. J. Edwards, A Treatise on the Integral Calculus with Applications, Examples and Problems II, Chelsea Publishing Company, New York, 1954.
  5. S. Garboury and A. K. Rathie,Evaluation of new class of double definite integrals, Preprint, 1-12, 2015.
  6. Y. S. Kim, S. Garboury, and A. K. Rathie, Applications of extended Watson's summation theorem, Preprint, 1-28, 2015.
  7. Y. S. Kim, M. A. Rakha, and A. K. Rathie, Extensions of certain classical summation theorems for the series $_2F_1$, $_3F_2$ and $_4F_3$ with applications in Ramanujan's summations, Int. J. Math. Math. Sci. (2010), 3095031, 26 papers.
  8. A. P. Prudnikov, Y. A. Brychkov, and O. I. Marichev, Integrals and Series. Vol. 3, More Special Functions, Gordon and Breach Science Publishers, New York, 1990.
  9. E. D. Rainville, Special Functions, Macmillan Company: New York; 1960: Reprinted by Chelsea Publishing Company, Bronx, New York, 1971.
  10. N. Rathie, Integrals involving H functions, Vijnana Parishad Anusandhan Patrika 22 (1979), no. 3, 253-258.
  11. L. J. Slater, Generalized Hypergeometric Functions, Cambridge University Press, Cambridge, London, and New York, 1966.
  12. H. M. Srivastava and J. Choi, Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier Science Publishers, Amsterdam, London, and New York, 2012.