호남수학학술지 (Honam Mathematical Journal)

  • 제38권2호
  • /
  • Pages.367-373
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  • 2016
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  • 1225-293X(pISSN)
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  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
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REPRESENTATIONS OF RAMANUJAN CONTINUED FRACTION IN TERMS OF COMBINATORIAL PARTITION IDENTITIES

  • 투고 : 2016.01.18
  • 심사 : 2016.02.18
  • 발행 : 2016.06.25
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초록

Adiga and Anitha [1] investigated the Ramanujan's continued fraction (18) to present many interesting identities. Motivated by this work, by using known formulas, we also investigate the Ramanujan's continued fraction (18) to give certain relationships between the Ramanujan's continued fraction and the combinatorial partition identities given by Andrews et al. [3].

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참고문헌

  1. C. Adiga and N. Anitha, A note on a continued fraction of Ramanujan, Bull. Austral. Math. Soc. 70 (2004), 489-497. https://doi.org/10.1017/S0004972700034742
  2. C. Adiga, B. C. Berndt, S. Bhargava and G. N. Watson, Theta functions and q-series (Chapter 16 of Ramanujan's second notebook), Mem. Amer. Math. Soc. 315 (1985), 1-91.
  3. G. E. Andrews, K. Bringman and K. Mahlburg, Double series representations for Schur's partition function and related identities, J. Combin. Theory Ser. A 132 (2015), 102-119. https://doi.org/10.1016/j.jcta.2014.12.004
  4. B. C. Berndt, Ramanujan's Notebooks, Part III, Springer-Verlag, Berlin, Heidelberg and New York, 1991.
  5. B. C. Berndt, Number Theory in the Sprit of Ramanujan, Amer. Math. Soc., Providence, Rhode Island, 2006.
  6. M. P. Chaudhary and J. Choi, Note on modular relations for Roger-Ramanujan type identities and representations for Jacobi identities, East Asian Math. J. 31(5) (2015), 659-665. https://doi.org/10.7858/eamj.2015.046
  7. H. M. Srivastava and M. P. Chaudhary, Some relationships between q-product identities, combinatorial partition identities and continued-fractions identities, Adv. Stud. Contemporary Math. 25(3) (2015), 265-272.
  8. 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.