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SOME EQUALITIES FOR CONTINUED FRACTIONS OF GENERALIZED ROGERS-RAMANUJAN TYPE

Xiantao Wang|Yongqun Li
대한수학회 (The Korean Mathematical Society)|2011.09|대한수학회지 (Journal of the KMS)|제48권 제5호|pp. 887-898

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참고문헌

키워드

equalityBauer-Muir transformationconvergence in the modified senseconvergence in the classical sense
주제분류수학

초록

In this paper, we rst discuss the convergence of the con-tinued fractions of generalized Rogers-Ramanujan type in the modi ed sense. Then we prove several equalities concerning these continued frac-tions. The proofs of our main results are mainly based on the Bauer-Muir transformation.

Abstract

In this paper, we rst discuss the convergence of the con-tinued fractions of generalized Rogers-Ramanujan type in the modi ed sense. Then we prove several equalities concerning these continued frac-tions. The proofs of our main results are mainly based on the Bauer-Muir transformation.

참고문헌 (10)

  1. K. Alladi, "On the modied convergence of some continued fractions of Rogers- Ramanujan type", J. Combin. Theory Ser. A, 65(2), pp.214~245 (1994)
  2. 강순이, "The Rogers-Ramanujan continued fraction", JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 105(1-2), pp.9~24
  3. B. C. Berndt, "Some theorem on the Rogers- Ramanujan continued fraction in Ramanujan's lost notebook", Trans. Amer. Math. Soc, 352(5), pp.2157~2177 (2000)
  4. B. C. Berndt, "On the generalized Rogers-Ramanujan continued fraction", Ramanujan J, 7(1), pp.321~331 (2003)
  5. L. Jacobsen, "On the Bauer-Muir transformation for continued fractions and its appli- cations", J. Math. Anal. Appl, 152(2), pp.496~514 (1990)
  6. W. B. Jones, "Continued Fractions: Analytic Theory and Applications, Encyclopedia of Mathematics and its Applications" (1980), Addison-Wesley
  7. J. Lee, "Modied convergence of Ramanujan type continued fractions", ~
  8. L. Lorentzen, "Continued Fractions with Applications, Studies in Computational Mathematics 3" (1992)
  9. S. Ramanujan, "The Lost Notebook and Other Unpublished Papers" (1988), Narosa
  10. W. J. Thron, "Modications of continued fractions, a survey, Analytic theory of continued fractions", Lecture Notes in Math, 932, pp.38~66 (1982), Springer

관련 논문AI추천

On certain continued fraction expansions for ratios of basic hypergeometric seriesK. R. Rajanna, K. R. Vasuki장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2007 · 제10권 제2호Certain identities for a continued fraction of RamanujanK. S. Bairy, M. S. M. Naika, S. Chandankumar장전수학회 · Advanced Studies in Contemporary Mathematics2014 · 제24권 제1호Evaluations of the Rogers-Ramanujan continued Fraction by Theta-function Identities Revisited백대현, Jinhee Yi한국수학교육학회 · 이론수학과 교직수학2022 · 제29권 제3호EVALUATIONS OF THE ROGERS-RAMANUJAN CONTINUED FRACTION BY THETA-FUNCTION IDENTITIES백대현한국수학교육학회 · 이론수학과 교직수학2021 · 제28권 제4호Special Case on Rogers-Ramanujan Type Continued Fraction IdentityB. N. DHARMENDRA장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2020 · 제23권 제3호Identities for the Rogers-Ramanujan continued fractionNayandeep Deka Baruah, Pranjal Talukdar대한수학회 · 대한수학회지2025 · 제62권 제1호

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