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EVALUATIONS OF THE ROGERS-RAMANUJAN CONTINUED FRACTION BY THETA-FUNCTION IDENTITIES

백대현
한국수학교육학회|2021.11|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제28권 제4호|pp. 377-386|DOI https://doi.org/10.7468/jksmeb.2021.28.4.377

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참고문헌

키워드

theta-functionmodular equationtheta-function identityRogers- Ramanujan continued fraction.
주제분류수학

초록

In this paper, we use theta-function identities involving parameters $l_{5,n}$, $l'_{5,n}$, and $l'_{5,4n}$ to evaluate the Rogers-Ramanujan continued fractions $R(e^{-2\pi\sqrt {n/20}})$ and $S(e^{-\pi\sqrt {n/5}})$ for some positive rational numbers $n$.

Abstract

In this paper, we use theta-function identities involving parameters $l_{5,n}$, $l'_{5,n}$, and $l'_{5,4n}$ to evaluate the Rogers-Ramanujan continued fractions $R(e^{-2\pi\sqrt {n/20}})$ and $S(e^{-\pi\sqrt {n/5}})$ for some positive rational numbers $n$.

참고문헌 (14)

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  3. B.C. Berndt, "Ramanujan's Notebooks, Part IV" (1994), Springer-Verlag
  4. B.C. Berndt, "Some values for the Rogers-Ramanujan continued fraction", Can. J. Math, 47(5), pp.897~914 (1995)
  5. B.C. Berndt, "Explicit evaluations of the Rogers-Ramanujan continued fraction", J. Reine Angew. Math, 480, pp.141~159 (1996)
  6. H. H. Chan, "On Ramanujan's cubic continued fraction", Acta Arith, 73, pp.343~355 (1995)
  7. 백대현, "On some modular equations of degree 5 and their applications", 대한수학회보, 50(4), pp.1315~1328 (2013), 대한수학회
  8. K. G. Ramanathan, "On Ramanujan's continued fraction", Acta Arith, 43, pp.209~226 (1984)
  9. K. G. Ramanathan, "On the Rogers-Ramanujan continued fraction", Proc. Indian Acad. Sci. Math. Sci, 93, pp.67~77 (1984)
  10. K. G. Ramanathan, "Ramanujan's continued fraction", Indian J. Pure Appl. Math, 16, pp.695~724 (1985)
  11. K. G. Ramanathan, "Some applications of Kronecker's limit formula", J. Indian Math. Soc, 52, pp.71~89 (1987)
  12. N. Saikia, "Some new general theorems for the explicit evaluations of the Rogers-Ramanujan continued fraction", Comput. Methods Funct. Theory, 13, pp.597~611 (2013)
  13. J. Yi, "Evaluations of the Rogers-Ramanujan continued fraction R(q) by modular equa-tions", Acta Arith, 97, pp.103~127 (2001)
  14. J. Yi, "The explicit formulas and evaluations of Ramanujan's theta-function", J. Math. Anal. Appl, 321, pp.157~181 (2006)

관련 논문AI추천

Evaluations of the Rogers-Ramanujan continued Fraction by Theta-function Identities Revisited백대현, Jinhee Yi한국수학교육학회 · 이론수학과 교직수학2022 · 제29권 제3호Identities for the Rogers-Ramanujan continued fractionNayandeep Deka Baruah, Pranjal Talukdar대한수학회 · 대한수학회지2025 · 제62권 제1호Evaluations of the cubic continued fraction by some theta function identities백대현, 이진희강원경기수학회 · 한국수학논문집2019 · 제27권 제4호Evaluations of the cubic continued fraction by some theta function identities: Revisited백대현한국수학교육학회 · 이론수학과 교직수학2021 · 제28권 제1호On some modular equations of degree 5 and their applications백대현, 이진희대한수학회 · 대한수학회보2013 · 제50권 제4호Relations Between Ramanujan's Cubic Continued Fraction and a Continued Fraction of Order 12 and its EvaluationsB. R. Srivatsa Kumar, H. C. Vidya경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2018 · 제58권 제2호

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