Table of Contents
ISRN Mathematical Analysis
Volume 2014, Article ID 410801, 6 pages
http://dx.doi.org/10.1155/2014/410801
Research Article

Contiguous Function Relations for -Hypergeometric Functions

Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan

Received 4 December 2013; Accepted 27 January 2014; Published 10 April 2014

Academic Editors: Y. S. Han and S. Zhang

Copyright © 2014 Shahid Mubeen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. E. D. Rainville, Special Functions, The Macmillan, New York, NY, USA, 1960. View at MathSciNet
  2. J.-L. Lavoie, F. Grondin, and A. K. Rathie, “Generalizations of Watson's theorem on the sum of a 3F2,” Indian Journal of Mathematics, vol. 34, no. 1, pp. 23–32, 1992. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. J. L. Lavoie, F. Grondin, and A. K. Rathie, “Generalizations of Whipple's theorem on the sum of a 3F2,” Journal of Computational and Applied Mathematics, vol. 72, no. 2, pp. 293–300, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. M. Abramowitz and I. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover, New York, NY, USA, 1972.
  5. P. Agarwal, “Contiguous relations for bilateral basic hypergeometric series,” International Journal of Mathematical Sciences, vol. 3, no. 2, pp. 375–388, 2004. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. G. E. Andrews, R. Askey, and R. Roy, Special Functions, Cambridge University Press, Cambridge, UK, 1999. View at MathSciNet
  7. G. Gasper and M. Rahman, Basic Hypergeometric Series, Encyclopedia of Mathematics and its Applications, Cambridge University Press, Cambridge, UK, 1990. View at MathSciNet
  8. D. P. Gupta and D. R. Masson, “Contiguous relations, continued fractions and orthogonality,” Transactions of the American Mathematical Society, vol. 350, no. 2, pp. 769–808, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. M. E. H. Ismail and C. A. Libis, “Contiguous relations, basic hypergeometric functions, and orthogonal polynomials. I,” Journal of Mathematical Analysis and Applications, vol. 141, no. 2, pp. 349–372, 1989. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. E. D. Rainville, “The contiguous function relations for pFq with applications to Bateman's Ju,vn and Rice's Hn(ζ;ρ;υ),” Bulletin of the American Mathematical Society, vol. 51, pp. 714–723, 1945. View at Publisher · View at Google Scholar · View at MathSciNet
  11. T. Morita, “Use of the gauss contiguous relations in computing the hypergeometric functions 2F1(n + 1/2, n + 1/2; m ; z),” Interdisciplinary Information Sciences, vol. 2, no. 1, pp. 63–74, 1996. View at Publisher · View at Google Scholar
  12. D. P. Gupta, M. E. H. Ismail, and D. R. Masson, “Contiguous relations, basic hypergeometric functions, and orthogonal polynomials. III. Associated continuous dual q-Hahn polynomials,” Journal of Computational and Applied Mathematics, vol. 68, no. 1-2, pp. 115–149, 1996. View at Publisher · View at Google Scholar · View at MathSciNet
  13. R. Vidunas, “A generalization of Kummer's identity,” The Rocky Mountain Journal of Mathematics, vol. 32, no. 2, pp. 919–936, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. R. Vidunas, “Contiguous relations of hypergeometric series,” Journal of Mathematical Analysis and Applications, vol. 135, pp. 507–519, 2003. View at Google Scholar
  15. M. A. Rakha and A. K. Ibrahim, “On the contiguous relations of hypergeometric series,” Journal of Computational and Applied Mathematics, vol. 192, no. 2, pp. 396–410, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. A. K. Ibrahim and M. A. Rakha, “Contiguous relations and their computations for 2F1 hypergeometric series,” Computers & Mathematics with Applications, vol. 56, no. 8, pp. 1918–1926, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. R. Díaz and C. Teruel, “q,k-generalized gamma and beta functions,” Journal of Nonlinear Mathematical Physics, vol. 12, no. 1, pp. 118–134, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. R. Díaz and E. Pariguan, “On hypergeometric functions and Pochhammer k-symbol,” Divulgaciones Matemáticas, vol. 15, no. 2, pp. 179–192, 2007. View at Google Scholar · View at MathSciNet
  19. R. Díaz, C. Ortiz, and E. Pariguan, “On the k-gamma q-distribution,” Central European Journal of Mathematics, vol. 8, no. 3, pp. 448–458, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  20. C. G. Kokologiannaki, “Properties and inequalities of generalized k-gamma, beta and zeta functions,” International Journal of Contemporary Mathematical Sciences, vol. 5, no. 13–16, pp. 653–660, 2010. View at Google Scholar · View at MathSciNet
  21. V. Krasniqi, “A limit for the k-gamma and k-beta function,” International Mathematical Forum, vol. 5, no. 33, pp. 1613–1617, 2010. View at Google Scholar · View at MathSciNet
  22. V. Krasniqi, “Inequalities and monotonicity for the ration of k-gamma functions,” Scientia Magna, vol. 6, no. 1, pp. 40–45, 2010. View at Google Scholar · View at MathSciNet
  23. F. Merovci, “Power product inequalities for the Γk function,” International Journal of Mathematical Analysis, vol. 4, no. 21–24, pp. 1007–1012, 2010. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. M. Mansour, “Determining the k-generalized gamma function Γk(x) by functional equations,” International Journal of Contemporary Mathematical Sciences, vol. 4, no. 21–24, pp. 1037–1042, 2009. View at Google Scholar · View at MathSciNet
  25. S. Mubeen and G. M. Habibullah, “k-fractional integrals and application,” International Journal of Contemporary Mathematical Sciences, vol. 7, no. 1–4, pp. 89–94, 2012. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  26. S. Mubeen and G. M. Habibullah, “An integral representation of some k-hypergeometric functions,” International Mathematical Forum, vol. 7, no. 1–4, pp. 203–207, 2012. View at Google Scholar · View at MathSciNet
  27. S. Mubeen, “Solution of some integral equations involving conuent k-hypergeometric functions,” Journal of Applied Mathematics, vol. 4, no. 7, pp. 9–11, 2013. View at Publisher · View at Google Scholar