호남수학학술지 (Honam Mathematical Journal)

  • 제38권4호
  • /
  • Pages.693-699
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  • 2016
  • /
  • 1225-293X(pISSN)
  • /
  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
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A DERIVATION OF TWO QUADRATIC TRANSFORMATIONS CONTIGUOUS TO THAT OF KUMMER VIA A DIFFERENTIAL EQUATION APPROACH

  • Shani, K. (Department of Mathematics, School of Mathematical and Physical Sciences,Central University of Kerala) ;
  • Choi, Junesang (Department of Mathematics, Dongguk University) ;
  • Rathie, Arjun K. (Department of Mathematics, School of Mathematical and Physical Sciences,Central University of Kerala)
  • 투고 : 2016.07.20
  • 심사 : 2016.10.14
  • 발행 : 2016.12.25
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초록

The purpose of this note is to provide an alternative proof of two quadratic transformations contiguous to that of Kummer using a differential equation approach.

키워드

참고문헌

  1. G. E. Andrews, R. Askey and R. Roy, Special Functions, Encyclopedia of Mathematics and its Applications 71, Cambridge University Press, Cambridge, 1999.
  2. Y. S. Kim, A quadratic transformation due to Kummer, Annals of Korea 16 (1999), 223-226.
  3. Y. S. Kim, M. A. Rakha and A. K. Rathie, Generalizations of Kummer's second theorem with applications, Comput. Math. Math. Phys. 50(3) (2010), 387-402. https://doi.org/10.1134/S0965542510030024
  4. Y. L. Luke, The Special Functions and their Approximations 1, Academic Press, New York, 1969.
  5. F. W. J. Olver, D. W. Lozier, R. F. Boisvert and C. W. Clark (editors), NIST Handbook of Mathematical Functions, National Institute of Standards and Technology and Cambridge University Press, 2010.