New representations for $\sigma(q)$ via reciprocity theorems

Koustav Banerjee; Atul Dixit

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arXiv · 1607.05651

New representations for $\sigma(q)$ via reciprocity theorems

Koustav Banerjee·Atul Dixit

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Abstract

Two new representations for Ramanujan's function $\sigma(q)$ are obtained. The proof of the first one uses the three-variable reciprocity theorem due to Soon-Yi Kang and a transformation due to R.P. Agarwal while that of the second uses the four-variable reciprocity theorem due to George Andrews and a generalization of a recent transformation of Andrews, Schultz, Yee and the second author. The advantage of these representations is that they involve free complex parameters - one in the first representation, and two in the second.

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Koustav Banerjee, Atul Dixit. 2016-07-19. New representations for $\sigma(q)$ via reciprocity theorems. https://arxiv.org/abs/1607.05651

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