논문KCI 등재
Note on Modular relations for the Roger-Ramanujan type identities and representations for Jacobian identity
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초록
Combining and specializing some known results,we establish six identities which depict six modular relations for the Roger-Ramanujan type identitiesand two equivalent representations for Jacobian identity expressed in terms of combinatorial partition identities and Ramanujan-Selberg continued fraction. Two q-product identities are also considered.
Abstract
Combining and specializing some known results,we establish six identities which depict six modular relations for the Roger-Ramanujan type identitiesand two equivalent representations for Jacobian identity expressed in terms of combinatorial partition identities and Ramanujan-Selberg continued fraction. Two q-product identities are also considered.
참고문헌 (11)
- G. E. Andrews, "Double series representations for Schur's partition function and related identities", J. Combin. Theory Ser. A, 132, pp.102~119 (2015)
- N. D. Baruah, "Modular relations for the nonic analogues of the Rogers-Ramanujan functions with applications to partitions", J. Number Theory, 128, pp.175~206 (2008)
- B. C. Berndt, "Ramanujan's Notebooks, Part III" (1991), Springer-Verlag
- M. P. Chaudhary, "Generalization of Ramanujan's identities in terms of q-products and continued fractions", Global J. Sci. Frontier Res. Math. Decision Sci, 12(2), pp.53~60 (2012)
- M. P. Chaudhary, "On q-product identities", Pacific J. Appl. Math, 5(2), pp.123~129 (2013)
- J. A. Ewell, "A note on a Jacobian identity", Proc. Amer. Math. Soc, 126, pp.421~423 (1998)
- H. Hahn, "Eisentein series, Analogues of the Ragers-Ramanujan function, and Partition identities", 박사, pp.2004
- S. Ramanujan, "Notebooks, 2 Volumes", Tata Institute of Fundamental Research, ~ (1957)
- A. Selberg, "Uber einige arithmetische Identitaten", Avh. Norske Vid.-Akad. Oslo I. Mat.-Naturv. Kl, 8, pp.323~ (1936)
- H. M. Srivastava, "Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier Science Publishers" (2012), Elsevier Science Publishers
- H. M. Srivastava, "Multiple Gaussian Hypergeometric Series" (1985), John Wiley and Sons
관련 논문AI추천
Identities for the Rogers-Ramanujan continued fractionNayandeep Deka Baruah, Pranjal Talukdar대한수학회 · 대한수학회지2025 · 제62권 제1호Evaluations of the Rogers-Ramanujan continued Fraction by Theta-function Identities Revisited백대현, Jinhee Yi한국수학교육학회 · 이론수학과 교직수학2022 · 제29권 제3호Special Case on Rogers-Ramanujan Type Continued Fraction IdentityB. N. DHARMENDRA장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2020 · 제23권 제3호On Certain New Modular Relations for the Rogers-Ramanujan type functions of order TwelveK. R. Vasuki, P. S. Guruprasad장전수학회 · Advanced Studies in Contemporary Mathematics2010 · 제20권 제3호Some Relationships Between q-Product Identities, Combinatorial Partition Identities and Continued-Fraction IdentitiesH. M. Srivastava, M. P. Chaudhary장전수학회 · Advanced Studies in Contemporary Mathematics2015 · 제25권 제3호Some algebraic relations for the Ramanujan's general $q$-continued fraction of order forty-twoBhat Chethan Shruthi, Raksha대한수학회 · 대한수학회논문집2025 · 제40권 제2호
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