Analysis of a generalized Lebesgue identity in Ramanujan’s Lost Notebook

We analyze a two-parameter q -series identity in Ramanujan’s Lost Notebook that generalizes the product part of the fundamental one-parameter Lebesgue identity. From reformulations of this two-parameter identity, we deduce new partition theorems including variants of the Gauss triangular number iden...

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Bibliographic Details
Published in:The Ramanujan journal 2012-12, Vol.29 (1-3), p.339-358
Main Author: Alladi, Krishnaswami
Format: Article
Language:English
Subjects:
Combinatorics
Field Theory and Polynomials
Fourier Analysis
Functions of a Complex Variable
Mathematics
Mathematics and Statistics
Number Theory
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Summary:We analyze a two-parameter q -series identity in Ramanujan’s Lost Notebook that generalizes the product part of the fundamental one-parameter Lebesgue identity. From reformulations of this two-parameter identity, we deduce new partition theorems including variants of the Gauss triangular number identity and Euler’s pentagonal number theorem. We discuss connections with a partial theta identity of Ramanujan and with several classical results such as those of Sylvester and Göllnitz–Gordon.
ISSN:1382-4090
1572-9303
DOI:10.1007/s11139-012-9380-z