The Rogers-Ramanujan Identities

Fazlee Hossain and Sabuj Das

MPRA Paper from University Library of Munich, Germany

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 Rogers-Ramanujan 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 Rogers-Ramanujan 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 Rogers-Ramanujan Identities with help of Ramanujan’s device of the introduction of a second parameter a.

Keywords: At most; auxiliary function; convenient; expansion; minimal difference; operator; Ramanujan’s device. (search for similar items in EconPapers)
JEL-codes: C3 C30 (search for similar items in EconPapers)
Date: 2015-03-12, Revised 2015-03-28
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Published in Turkish Journal of Analysis and Number Theory 2.3(2015): pp. 37-42

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