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Continued fractions of order six and new Eisenstein series identities. (English) Zbl 1423.11022

Summary: We prove two identities for Ramanujan’s cubic continued fraction and a continued fraction of Ramanujan, which are analogues of Ramanujan’s identities for the Rogers-Ramanujan continued fraction. We further derive Eisenstein series identities associated with Ramanujan’s cubic continued fraction and Ramanujan’s continued fraction of order six.

MSC:

11A55 Continued fractions
11P84 Partition identities; identities of Rogers-Ramanujan type
11F11 Holomorphic modular forms of integral weight
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