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TWO GENERAL HYPERGEOMETRIC TRANSFORMATION FORMULAS

  • Choi, Junesang (Department of Mathematics Dongguk University) ;
  • Rathie, Arjun K. (Department of Mathematics School of Mathematical and Physical Sciences Central University of Kerala)
  • 투고 : 2014.04.10
  • 발행 : 2014.10.31

초록

A large number of summation and transformation formulas involving (generalized) hypergeometric functions have been developed by many authors. Here we aim at establishing two (presumably) new general hypergeometric transformations. The results are derived by manipulating the involved series in an elementary way with the aid of certain hypergeometric summation theorems obtained earlier by Rakha and Rathie. Relevant connections of certain special cases of our main results with several known identities are also pointed out.

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참고문헌

  1. W. N. Bailey, Generalized Hypergeometric Series, Cambridge University Press, Cambridge, 1935; Reprinted by Stechert Hafner, New York, 1964.
  2. J. Choi, A. K. Rathie, and H. M. Srivastava, A generalization of a formula due to Kummer, Integral Transforms Spec. Funct. 22 (2011), no. 11, 851-859. https://doi.org/10.1080/10652469.2011.588786
  3. J. Choi, A. K. Rathie, and H. M. Srivastava, Certain hypergeometric identities deducible by using the beta integral method, Bull. Korean Math. Soc. 50 (2013), no. 5, 1673-1681. https://doi.org/10.4134/BKMS.2013.50.5.1673
  4. Y. S. Kim and A. K. Rathie, Applications of a generalized form of Gauss's second theorem to the series $_{3}F_{2}$, Math. Commun. 16 (2011), no. 2, 481-489.
  5. Y. S. Kim, M. A. Rakha, and A. K. Rathie, Extensions of certain classical summation theorems for the series $_{2}F_{1}$, $_{3}F_{2}$, and $_{4}F_{3}$ with applications in Ramanujan's summa- tions, Int. J. Math. Sci. 2010 (2010), Art. ID 309503, 26 pp.
  6. J. L. Lavoie, F. Grondin, and A. K. Rathie, Generalizations of Whipple's theorem on the sum of a $_{3}F_{2}$, J. Comput. Appl. Math. 72 (1996), no. 2, 293-300. https://doi.org/10.1016/0377-0427(95)00279-0
  7. E. D. Rainville, Special Functions, Macmillan Company, New York, 1960; Reprinted by Chelsea Publishing Company, Bronx, New York, 1971.
  8. M. A. Rakha and A. K. Rathie, Generalizations of classical summation theorems for the series $_{2}F_{1}$ and $_{3}F_{2}$ with applications, Integral Transforms Spec. Funct. 22 (2011), no. 11, 823-840. https://doi.org/10.1080/10652469.2010.549487
  9. L. J. Slater, Generalized Hypergeometric Functions, Cambridge University Press, Cambridge, London, and New York, 1966.
  10. H. M. Srivastava and J. Choi, Series Associated with the Zeta and Related Functions, Kluwer Academic Publishers, Dordrecht, Boston and London, 2001.
  11. 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.