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ON SOME CIRCULAR SUMMATION FORMULAS FOR THETA FUNCTIONS

YUDHISTHIRA JAMUDULIA|S. N. FATHIMA
장전수학회 (Jangjeon Mathematical Society)|2017.01|Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집) (Proceedings of the Jangjeon Mathematical Society)|제20권 제1호|pp. 23-34|DOI 10.17777/pjms.2017.20.1.004

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참고문헌

키워드

Theta functionsCircular summationElliptic functions
주제분류수학

초록

In his lost notebook, Ramanujan claimed that the "circular" summation of nth power of his symmetric theta function f(a, b) satisfies a factorization of the form f(a, b)F(ab). In this paper, we obtain new circular summation formula of theta functions using the theory of elliptic functions. As an application, we also obtain few interesting identity of the theta functions.

Abstract

In his lost notebook, Ramanujan claimed that the "circular" summation of nth power of his symmetric theta function f(a, b) satisfies a factorization of the form f(a, b)F(ab). In this paper, we obtain new circular summation formula of theta functions using the theory of elliptic functions. As an application, we also obtain few interesting identity of the theta functions.

참고문헌 (23)

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관련 논문AI추천

ON SOME PARTIAL THETA FUNCTION IDENTITIES OF RAMANUJAN FOUND IN HIS LOST NOTEBOOKD. D. Somashekara, H. I. Kwon, S. L. Shalini, T. Kim장전수학회 · Advanced Studies in Contemporary Mathematics2015 · 제25권 제1호ON SOME NEW MODULAR RELATIONS FOR RAMANUJAN'S REMARKABLE PRODUCT OF THETA FUNCTIONSB. HEMANTHKUMAR, M. S. MAHADEVA NAIKA, S. Chandankumar장전수학회 · Advanced Studies in Contemporary Mathematics2013 · 제23권 제3호CERTAIN MODULAR RELATIONS FOR REMARKABLE PRODUCT OF THETA-FUNCTIONSK. Sushan Bairy, M. S. MAHADEVA NAIKA, N. P. SUMAN장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2014 · 제17권 제3호On some identities of Ramanujan found in his lost notebookD.D. Somashekara, D. Mamta장전수학회 · Advanced Studies in Contemporary Mathematics2008 · 제16권 제2호A note on modular equations of signature 2 and their evaluationsArjun Kumar Rathie, Belakavadi Radhakrishna Srivatsa Kumar, Nagara Vinayaka Udupa Sayinath, SHRUTHI대한수학회 · 대한수학회논문집2022 · 제37권 제1호New identities for ratios of Ramanujan’s theta functionK. Sushan Bairy, M. S. MAHADEVA NAIKA, S. Chandankumar장전수학회 · Advanced Studies in Contemporary Mathematics2017 · 제27권 제1호

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