대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제32권2호
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  • Pages.321-332
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  • 2017
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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SOME INTEGRAL REPRESENTATIONS AND TRANSFORMS FOR EXTENDED GENERALIZED APPELL'S AND LAURICELLA'S HYPERGEOMETRIC FUNCTIONS

  • Kim, Yongsup (Department of Mathematics Education Wonkwang University)
  • 투고 : 2016.04.01
  • 발행 : 2017.04.30
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초록

In this paper, we generalize the extended Appell's and Lauricella's hypergeometric functions which have recently been introduced by Liu [9] and Khan [7]. Also, we aim at establishing some (presumbly) new integral representations and transforms for the extended generalized Appell's and Lauricella's hypergeometric functions.

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참고문헌

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  7. N. U. Khan and M. Ghayasuddin, Generalization of extended Appell's and Lauricella's hypergeometric functions, Honam Math. J. 37 (2015), no. 1, 113-126. https://doi.org/10.5831/HMJ.2015.37.1.113
  8. D. M. Lee, A. K. Rathie, R. K. Parmar, and Y. S. Kim, Generalization of extended beta function, hypergeometric and confluent hypergeometric functions, Honam Math. J. 33 (2011), no. 2, 187-206. https://doi.org/10.5831/HMJ.2011.33.2.187
  9. H. Liu, Some generating relations for extended Appell's and Lauricella hypergeometric functions, Rocky Moutain J. Math. 41 (2014), no. 6, 1987-2007.
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  12. E. Ozergin, M. A. Ozarslan, and A. Altin, Extension of gamma, beta and hypergeometric functions, J. Comput. Appl. Math. 235 (2011), no. 16, 4601-4610. https://doi.org/10.1016/j.cam.2010.04.019
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  14. H. M. Srivastava, P. Agawal, and R. Jain, Generating functions for the generalized Gauss hypergeometric functions, Appl. Math. Comput. 247 (2014), 348-352.
  15. H. M. Srivastava and J. Choi, Zeta and q-Zeta Functions and Associated Series and Integrals, Elsvier Science Publishers, Amsterdam, London and New York, 2012.
  16. H.M. Srivastava and H. L.Manocha, A Treatise on Generating Functions, Ellis Horwood Limited, 1984.
  17. R. Vidunas, Specialization of Appell's functions to univariate hypergeometric functions, J. Math. Anal. Appl. 355 (2009), no. 1, 145-163. https://doi.org/10.1016/j.jmaa.2009.01.047
  18. Wolfram Research, Inc., Hypergeometric $_1F_1$, at http://functions.wolfram.com/HypergeometricFunctions/Hypergeometric$_1F_1$/.

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