Hossain, Fazlee and Das, Sabuj (2015): The RogersRamanujan Identities. Published in: Turkish Journal of Analysis and Number Theory , Vol. 3, No. 2 (1 April 2015): pp. 3742.

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Abstract
In 1894, Rogers found the two identities for the first time. In 1913, Ramanujan found the two identities later and then the two identities are known as The RogersRamanujan Identities. In 1982, Baxter used the two identities in solving the Hard Hexagon Model in Statistical Mechanics. In 1829 Jacobi proved his triple product identity; it is used in proving The RogersRamanujan Identities. In 1921, Ramanujan used Jacobi’s triple product identity in proving his famous partition congruences. This paper shows how to generate the generating function for , , and , and shows how to prove the Corollaries 1 and 2 with the help of Jacobi’s triple product identity. This paper shows how to prove the Remark 3 with the help of various auxiliary functions and shows how to prove The RogersRamanujan Identities with help of Ramanujan’s device of the introduction of a second parameter a.
Item Type:  MPRA Paper 

Original Title:  The RogersRamanujan Identities 
English Title:  The RogersRamanujan Identities 
Language:  English 
Keywords:  At most, auxiliary function, convenient, expansion, minimal difference, operator, Ramanujan’s device. 
Subjects:  C  Mathematical and Quantitative Methods > C3  Multiple or Simultaneous Equation Models ; Multiple Variables C  Mathematical and Quantitative Methods > C3  Multiple or Simultaneous Equation Models ; Multiple Variables > C30  General 
Item ID:  83043 
Depositing User:  Haradhan Kumar Mohajan 
Date Deposited:  01 Dec 2017 09:47 
Last Modified:  26 Sep 2019 08:56 
References:  [1] Andrews, G.E, “An Introduction to Ramanujan’s Lost Notebook”, American Mathmatical Monthly, 86: 89–108. 1979. [2] Hardy, G.H. and Wright, E.M. “Introduction to the Theory of Numbers”, 4th Edition, Oxford, Clarendon Press, 1965. [3] Jacobi, C.G.J. (1829), “Fundamenta Nova Theoriae Functionum Ellipticarum (in Latin), Konigsberg Borntraeger”, Cambridge University Press, 2012. [4] Baxter, R.J., “Exactly Solved Model in Statistical Models”, London, Academic Press, 1982. [5] Ramanujan, S., “Congruence Properties of Partitions”, Math, Z. 9: 147–153. 1921. [6] Ramanujan, S., “Some Properties of P(n), Number of Partitions of n”, Proc. of the Cam. Philo. Society XIX, 207–210. 1919. [7] Das, S. and Mohajan, H.K., “Generating Function for P(n,p,*) and P(n, *,p)”, Amer. Rev. of Math. and Sta. 2(1): 33–35. 2014. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/83043 