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Evaluations of the cubic continued fraction by some theta function identities
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In this paper, we use some theta function identities involving two parameters $h_{n,k}$ and $h'_{n,k}$ for the theta function $\varphi$ to establish new evaluations of Ramanujan's cubic continued fraction.
Abstract
In this paper, we use some theta function identities involving two parameters $h_{n,k}$ and $h'_{n,k}$ for the theta function $\varphi$ to establish new evaluations of Ramanujan's cubic continued fraction.
참고문헌 (15)
- C. Adiga, "On Ra-manujan's cubic continued fraction and explicit evaluations of theta-functions", Indian J. pure appl. Math, 35(9), pp.1047~1062 (2004)
- C. Adiga, "Some new explicit evalua-tions of Ramanujan's cubic continued fraction", New Zealand J. Math, 31, pp.109~114 (2002)
- G. E. Andrews, "Ramanujan's lost notebook" (2000), Springer
- B. C. Berndt, "Ramanujan's notebooks, Part III" (1991), Springer-Verlag
- B. C. Berndt, "Ramanujan's notebooks, Part IV" (1994), Springer-Verlag
- B. C. Berndt, "Zhang Ramanujan's class invariants and cubic continued fraction", Acta Arith, 73, pp.67~85 (1995)
- H. H. Chan, "On Ramanujan's cubic continued fraction", Acta Arith, 73, pp.343~355 (1995)
- 백대현, "On some modular equations and their applications II", 대한수학회보, 50(4), pp.1221~1233 (2013), 대한수학회
- Dae Hyun Paek, "On evaluations of the cubic continued fraction by modular equations of degree 9", 순수 및 응용수학, 23(3), pp.223~236 (2016), 한국수학교육학회
- Dae Hyun Paek, "ON EVALUATIONS OF THE CUBIC CONTINUED FRACTION BY MODULAR EQUATIONS OF DEGREE 3", 순수 및 응용수학, 25(1), pp.17~29 (2018), 한국수학교육학회[DOI]
- K. G. Ramanathan, "On Ramanujan's continued fraction", Acta Arith, 43, pp.209~226 (1984)
- J. Yi, "The construction and applications of modular equations", Ph.D., pp.2001
- J. Yi, "Theta-function identities and the explicit formulas for theta-function and their applications", J. Math. Anal. Appl., 292, pp.381~400 (2004)
- 이진희, "On Some Modular Equations and Their Applications I", 대한수학회보, 50(3), pp.761~776 (2013), 대한수학회
- J. Yi, "The explicit formulas and evaluations of Ra-manujan's theta-function", J. Math. Anal. Appl., 321, pp.157~181 (2006)
관련 논문AI추천
Evaluations of the cubic continued fraction by some theta function identities: Revisited백대현한국수학교육학회 · 이론수학과 교직수학2021 · 제28권 제1호Relations 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 제2호Evaluations of the Rogers-Ramanujan continued Fraction by Theta-function Identities Revisited백대현, Jinhee Yi한국수학교육학회 · 이론수학과 교직수학2022 · 제29권 제3호On Evaluations of the Cubic Continued Fraction by Modular Equations of Degree 3 Revisited백대현, 안지원, 이강훈, 이진희한국수학교육학회 · 이론수학과 교직수학2024 · 제31권 제2호Some more relations on Ramanujan's cubic continued fraction and a continued fraction of order 12B. R. S. Kumar, H. C. Vidya장전수학회 · Advanced Studies in Contemporary Mathematics2014 · 제24권 제2호EVALUATIONS OF THE ROGERS-RAMANUJAN CONTINUED FRACTION BY THETA-FUNCTION IDENTITIES백대현한국수학교육학회 · 이론수학과 교직수학2021 · 제28권 제4호
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