Combinatorial Proofs of Identities in Ramanujan’s Lost Notebook Associated with the Rogers–fine Identity and False Theta Functions
نویسندگان
چکیده
Ramanujan’s lost notebook contains several identities arising from the Rogers–Fine identity and/or Rogers’ false theta functions. Combinatorial proofs for many of these identities are given.
منابع مشابه
Ramanujan's lost notebook: Combinatorial proofs of identities associated with Heine's transformation or partial theta functions
Combinatorial proofs are given for certain entries in Ramanujan’s lost notebook. Bijections of Sylvester, Franklin, and Wright, and applications of Algorithm Z of Zeilberger are employed. A new bijection, involving the new concept of the parity sequence of a partition, is used to prove one of Ramanujan’s fascinating identities for a partial theta function.
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