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ON THE SERIES EXPANSION OF THE RAMANUJAN'S CONTINUED FRACTION OF ORDER SIX

C. ADIGA|A. Vanitha|M. S. Surekha
장전수학회 (Jangjeon Mathematical Society)|2015.07|Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집) (Proceedings of the Jangjeon Mathematical Society)|제18권 제3호|pp. 343-352|DOI 10.17777/pjms.2015.18.3.011

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참고문헌

키워드

Continued fractionsdissectionspartitionscolored partitions
주제분류수학

초록

We give 3- and 6-dissections of Ramanujan's continued fraction of order six and its reciprocal. We also give combinatorial interpretations of the coefficients in the series expansions of the Ramanujan's continued fraction of order six and its reciprocal. These combinatorial results enable us to determine the signs of the coefficients.

Abstract

We give 3- and 6-dissections of Ramanujan's continued fraction of order six and its reciprocal. We also give combinatorial interpretations of the coefficients in the series expansions of the Ramanujan's continued fraction of order six and its reciprocal. These combinatorial results enable us to determine the signs of the coefficients.

참고문헌 (16)

  1. C. Adiga, "Chapter 16 of Ramanujan's second notebook: Theta functions and q-series", Mem. Amer. Math. Soc., 315, pp.1~91 (1985)
  2. C. Adiga, "On some modular relations and 2- and 4-dissections of Ramanujan's continued fraction of order six", Indian J. Math., 57(2), pp.199~216 (2015)
  3. G. E. Andrews, "Ramanujan's "Lost" notebook III. The Rogers-Ramanujan continued fraction", Adv. Math., 41, pp.186~208 (1981)
  4. G. E. Andrews, "Vanishing coefficients in infinite product expansions", J. Aust. Math. Soc., 27, pp.199~202 (1979)
  5. S. H. Chan, "The periodicity of the signs of the coefficients of certain infinite products", Pacific J. Math., 225, pp.13~32 (2006)
  6. M. D. Hirschhorn, "On the expansion of Ramanujan's continued fraction", Ramanujan J., 2, pp.521~527 (1998)
  7. M. D. Hirschhorn, "On the expansion of a continued fraction of Gordon", Ramanujan J., 5, pp.369~375 (2001)
  8. M. D. Hirschhorn, "On the 2- and 4-dissections of Ramanujan's continued fraction and its reciprocal", Ramanujan J., 24, pp.85~92 (2011)
  9. M. D. Hirschhorn, "On the 2-, 3-, 4- and 6-dissections of Ramanujan's cubic continued fraction and its reciprocal, in Proc. Ramanujan Rediscovered", RMS Lecture Note Series, 14, pp.125~138 (2009), Ramanujan Mathematical Society
  10. R. P. Lewis, "A conjecture of Hirschhorn on the 4-dissection of Ra-manujan's continued fraction", Ramanujan J., 4, pp.347~352 (2000)
  11. B. L. S. Lin, "On the expansion of a continued fraction of order twelve", Int. J. Number Thy., 9(8), pp.2019~2031 (2013)
  12. S. Ramanujan, "The Lost Notebook and Other Unpublished Papers" (1988), Narosa
  13. B. Richmond, "The Taylor coecients of certain in nite products", Acta Sci. Math., 40, pp.347~369 (1978)
  14. B. Srivastava, "On the 2-dissection and 4-dissection of Ramanujan's cubic continued fraction and identities", Tamusi Oxford J. Math. Sci., 23, pp.305~315 (2007)
  15. K. R. Vasuki, "On the series expansion of the Ramanujan cubic continued fraction", International J. Math. Combin, 4, pp.84~95 (2011)
  16. O. X. M. Yao, "On the 4-dissection of certain in nite products", Ramanujan J., 30, pp.1~7 (2013)

관련 논문AI추천

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