Ramanujan's "Lost" notebook IX: The partial theta function as an entire function

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Abstract

We establish the infinite product expansion for ∑n≥0anqn2. This is a corrected version of theexpansion stated in Ramanujan's "Lost" Notebook. The proof requires the study of a newfamily of polynomials which while not orthogonal have many similar properties.

Original languageEnglish (US)
Pages (from-to)408-422
Number of pages15
JournalAdvances in Mathematics
Volume191
Issue number2
DOIs
StatePublished - Mar 1 2005

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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