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Circular summation of theta functions in Ramanujan's Lost Notebook |
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| Authors: | Heng Huat Chan Zhi-Guo Liu Say Tiong Ng |
| Institution: | a National University of Singapore, Department of Mathematics, 2 Science Drive 2, Singapore 117543 b Massey University, Albany Campus, Private Bag 102 904, North Shore Mail Centre, Auckland, New Zealand c East China Normal University, Department of Mathematics, Shanghai 200062, PR China |
| 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. |
| Keywords: | Circular summation Elliptic Theta Ramanujan Jacobi Dixon |
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