Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

SOME INTEGRAL REPRESENTATIONS AND TRANSFORMS FOR EXTENDED GENERALIZED APPELL'S AND LAURICELLA'S HYPERGEOMETRIC FUNCTIONS

  • Kim, Yongsup (Department of Mathematics Education Wonkwang University)
  • Received : 2016.04.01
  • Published : 2017.04.30
Download PDF
⟨ Previous Next ⟩

Abstract

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.

Keywords

References

  1. P. Agarwal, J. Choi, and S. Jain, Extended hypergeometric functions of two and three variables, Commun. Korean Math. Soc. 30 (2015), no. 4, 403-414. https://doi.org/10.4134/CKMS.2015.30.4.403
  2. G. E. Andrews, R. Askey, and R. Roy, Special Functions, Cambridge University Press, Cambridge, 1999.
  3. M. A. Chaudhry, A. Qadir, M. Rafique, and S. M. Zubair, Extension of Euler's beta function, J. Comput. Appl. Math. 78 (1997), no. 1, 19-32. https://doi.org/10.1016/S0377-0427(96)00102-1
  4. M. A. Chaudhry, A. Qadir, H. M. Srivastava, and R. B. Paris, Extended hypergeometric and confluent hypergeometric function, Appl. Math. Comput. 159 (2004), no. 2, 589-602. https://doi.org/10.1016/j.amc.2003.09.017
  5. A. Hasanov and M. Turaev, Some decomposition formulas associated with the Lauricella function $F_{A}^{(r)}$ and other multiple hypergeometric functions, Appl. Math. Comput. 187 (2007), 195-201.
  6. A. Hasanov and M. Turaev, Decomposition formulas associated with the Lauricella multivariable hypergeo-metric functions, Comput. Math. Appl. 53 (2007), no. 7, 1119-1128. https://doi.org/10.1016/j.camwa.2006.07.007
  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.
  10. M. J. Luo, G. V. Milovanovic, and P. Agawal, Some results on the extended beta and extended hypergeometric functions, Appl. Math. Comput. 248 (2014), 631-651.
  11. M. A. Ozarslan and E. Ozergin, Some generating relations for extended hypergeometric functions via generalized fractional derivative operator, Math. Comp. Model. 52 (2010), no. 9-10, 1825-1833. https://doi.org/10.1016/j.mcm.2010.07.011
  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
  13. E. D. Rainville, Special Functions, Macmillan, New York, 1960.
  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$_1F_1$/.

Cited by

  1. Change-point detection and bootstrap for Hilbert space valued random fields vol.155, 2017, https://doi.org/10.1016/j.jmva.2017.01.007