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The Rogers-Ramanujan continued fraction and a new Eisenstein series identity |
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| Authors: | Heng Huat Chan |
| Institution: | a Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 119260, Republic of Singapore b Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Republic of Singapore c Department of Mathematics, East China Normal University, 500 Dongchuan Road, Shanghai 200241, PR China |
| Abstract: | With two elementary trigonometric sums and the Jacobi theta function θ1, we provide a new proof of two Ramanujan's identities for the Rogers-Ramanujan continued fraction in his lost notebook. We further derive a new Eisenstein series identity associated with the Rogers-Ramanujan continued fraction. |
| Keywords: | 33E05 11F11 11F20 11F27 |
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