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Some modular relations for the Roger-Ramanujan type functions of order six and its applications to partitions
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Some modular relations for the Roger-Ramanujan type functionsof order six and its applications to partitions
Abstract
Some modular relations for the Roger-Ramanujan type functionsof order six and its applications to partitions
참고문헌 (17)
- C. Adiga, "Chapter 16 of Ramanujan's second notebook: Theta functions and q-series", Mem. Amer. Math. Soc., 315, pp.1~91 (1985)
- C. Adiga, "Some new modular relations for the cubic functions", South East Asian Bull. Math., 36, pp.1~19 (2012)
- G. E. Andrews, "An Introduction to Ramanujan's \Lost" Notebook", Amer. Math. Monthly, 86, pp.89~108 (1976)
- B. C. Berndt, "Ramanujan's Notebooks, Part III" (1991), Springer-Verlag
- B. C. Berndt, "Ramanujan's forty identities for the Rogers-Ramanujan functions", Mem. Amer. Math. Soc., 188(880), pp.1~96 (2007)
- A. J. F. Biagioli, "A proof of some identities of Ramanujan using modular functions", Glasgow. Math. J., 31, pp.271~295 (1989)
- D. Bressoud, "Proof and generalization of certain identities conjectured by Ramanujan", Ph.D., pp.1977
- D. Hickerson, "A proof of the mock theta conjectures", Invent. Math, 94, pp.639~660 (1988)
- S. Ramanujan, "Proof of certain identities in combinatory analysis", Proc. Cambridge Philos. Soc., 19, pp.214~216 (1919)
- S. Ramanujan, "Algebraic relations between certain innite products", Proc. Lond. Math. Soc, 2 (1920)
- S. Ramanujan, "Collected Papers" (1927), Cambridge University Press
- L. J. Rogers, "Second memoir on the expansion of certain innite products", Proc. London Math. Soc., 25, pp.318~343 (1894)
- L. J. Rogers, "On a type of modular relation", Proc. London Math. Soc., 19(2), pp.387~397 (1921)
- L. J. Slater, "Further identities of Rogers-Ramanujan type", London Math. Soc., 54(2), pp.147~167 (1952)
- K. R. Vasuki, "Two modular equations for squares of the cubic-functions with applications", Note di Mathematica, 30, pp.61~70 (2010)
- G. N.Watson, "Proof of certain identities in combinatory analysis", J. Indian Math. Soc., 20, pp.57~69 (1933)
- H. Yesilyurt, "A generalization of a modular identity of Rogers", J. Number Thy., 129, pp.1256~1271 (2009)
관련 논문AI추천
On 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 THETA-FUNCTION IDENTITIES OF LEVEL SIX AND ITS APPLICATIONS TO PARTITIONSANUSHA KUMARI, B. R. SRIVATSA KUMAR장전수학회 · Advanced Studies in Contemporary Mathematics2018 · 제28권 제1호Certain relations for mock theta functions of order eightMaheshwar Pathak, Pankaj Srivastava대한수학회 · 대한수학회논문집2009 · 제24권 제4호Note on Modular relations for the Roger-Ramanujan type identities and representations for Jacobian identity최준상, M.P.Chaudhary영남수학회 · East Asian Mathematical Journal2015 · 제31권 제5호SOME NEW GENERAL CONGRUENCE PROPERTIES FOR pr(n)A. Anand, P. Murugan, S. N. Fathima장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2024 · 제27권 제4호SOME MODULAR RELATIONS BETWEEN RAMANUJAN’S FUNCTION V(q) AND V(qn)B. N. DHARMENDRA, M. C. MAHESH KUMAR장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2020 · 제23권 제3호
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