DOI QR코드

DOI QR Code

EXTENDED HYPERGEOMETRIC FUNCTIONS OF TWO AND THREE VARIABLES

  • AGARWAL, PRAVEEN (Department of Mathematics Anand International College of Engineering) ;
  • CHOI, JUNESANG (Department of Mathematics Dongguk University) ;
  • JAIN, SHILPI (Department of Mathematics Poornima College of Engineering)
  • Received : 2014.11.25
  • Published : 2015.10.31

Abstract

Extensions of some classical special functions, for example, Beta function B(x, y) and generalized hypergeometric functions $_pF_q$ have been actively investigated and found diverse applications. In recent years, several extensions for B(x, y) and $_pF_q$ have been established by many authors in various ways. Here, we aim to generalize Appell's hypergeometric functions of two variables and Lauricella's hypergeometric function of three variables by using the extended generalized beta type function $B_p^{({\alpha},{\beta};m)}$ (x, y). Then some properties of the extended generalized Appell's hypergeometric functions and Lauricella's hypergeometric functions are investigated.

Keywords

References

  1. P. Agarwal, Certain properties of the generalized Gauss hypergeometric functions, Appl. Math. Inf. Sci. 8 (2014), no. 5, 2315-2320. https://doi.org/10.12785/amis/080526
  2. M. A. Chaudhry, A. Qadir, M. Rafique, and S. M. Zubair, Extension of Euler beta function, J. Comput. Appl. Math. 78 (1997), no. 1, 19-32. https://doi.org/10.1016/S0377-0427(96)00102-1
  3. M. A. Chaudhry, A. Qadir, H. M. Srivastava, and R. B. Paris, Extended hypergeometric and confluent hypergeometric functions, Appl. Math. Comput. 159 (2004), no. 2, 589-602. https://doi.org/10.1016/j.amc.2003.09.017
  4. 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
  5. H. Liu and W. Wang, Some generating relations for extended Appell's and Lauricella's hypergeometric functions, Rocky Mountain J. Math., in press.
  6. M.-J. Luo, G. V. Milovanovic, and P. Agarwal, Some results on the extended beta and extended hypergeometric functions, Appl. Math. Comput. 248 (2014), 631-651. https://doi.org/10.1016/j.amc.2014.09.110
  7. E. Ozergin, Some properties of hypergeometric functions, Ph.D. Thesis, Eastern Mediterranean University, North Cyprus, February 2011.
  8. 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
  9. 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.
  10. H. M. Srivastava and P. W. Karlsson, Multiple Gaussian Hypergeometric Series, Ellis Horwood Limited, 1985.

Cited by

  1. Generating relations and multivariable Aleph-function vol.38, pp.3, 2018, https://doi.org/10.1515/anly-2017-0054