Circular summation of theta functions in Ramanujan's Lost Notebook

Please use this identifier to cite or link to this item: https://doi.org/10.1016/j.jmaa.2005.05.015

Title:	Circular summation of theta functions in Ramanujan's Lost Notebook
Authors:	Chan, H.H. Liu, Z.-G. Ng, S.T.
Keywords:	Circular summation Dixon Elliptic Jacobi Ramanujan Theta
Issue Date:	15-Apr-2006
Citation:	Chan, H.H., Liu, Z.-G., Ng, S.T. (2006-04-15). Circular summation of theta functions in Ramanujan's Lost Notebook. Journal of Mathematical Analysis and Applications 316 (2) : 628-641. ScholarBank@NUS Repository. https://doi.org/10.1016/j.jmaa.2005.05.015
Abstract:	In this paper, we prove Ramanujan's circular summation formulas previously studied by S.S. Rangachari, S.H. Son, K. Ono, S. Ahlgren and K.S. Chua using properties of elliptic and theta functions. We also derive identities similar to Ramanujan's summation formula and connect these identities to Jacobi's and Dixon's elliptic functions. At the end of the paper, we discuss the connection of our results with the recent thesis of E. Conrad. © 2005 Elsevier Inc. All rights reserved.
Source Title:	Journal of Mathematical Analysis and Applications
URI:	http://scholarbank.nus.edu.sg/handle/10635/102988
ISSN:	0022247X
DOI:	10.1016/j.jmaa.2005.05.015
Appears in Collections:	Staff Publications

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