Ramanujan's “Lost” notebook IX: the partial theta function as an entire function
نویسندگان
چکیده
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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is the Legendre symbol. As a matter of fact we can talk about a single identity (cf. [C2]) because (1.3) can be obtained from (1.2) by applying a Hecke’s result (see, for instance, p. 119 [My]). By now there are several proofs of (1.2) and (1.3) in the literature. The first proof was given by Bailey ([B1] and [B2]) by using the 6Ψ6–summation. For recent proofs see, for instance, [Rg], [C1] and ...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2005
ISSN: 0001-8708
DOI: 10.1016/j.aim.2004.03.013