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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Some new observations on the Göllnitz-Gordon and Rogers-Ramanujan identities


Author: Krishnaswami Alladi
Journal: Trans. Amer. Math. Soc. 347 (1995), 897-914
MSC: Primary 11P82; Secondary 05A30, 11B65, 11P81, 33D10
MathSciNet review: 1284910
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Abstract: Two new, short and elementary proofs of the Göllnitz-Gordon identities are presented by considering the odd-even split of the Euler Pentagonal Series and the Triangular Series of Gauss. Using this approach the equality of certain shifted partition functions are established. Next, the odd and even parts of the famous Rogers-Ramanujan series are shown to have interesting product representations ($ \bmod 80$). From this, new shifted partition identities are derived.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1995-1284910-4
PII: S 0002-9947(1995)1284910-4
Keywords: Göllnitz-Gordon identities, Rogers-Ramanujan identities, odd-even split, shifted partition identities
Article copyright: © Copyright 1995 American Mathematical Society