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Archive for History of Exact Sciences

, Volume 64, Issue 3, pp 301–373 | Cite as

A summary of Euler’s work on the pentagonal number theorem

  • Jordan BellEmail author
Article

Abstract

In this article, we give a summary of Leonhard Euler’s work on the pentagonal number theorem. First we discuss related work of earlier authors and Euler himself. We then review Euler’s correspondence, papers and notebook entries about the pentagonal number theorem and its applications to divisor sums and integer partitions. In particular, we work out the details of an unpublished proof of the pentagonal number theorem from Euler’s notebooks. As we follow Euler’s discovery and proofs of the pentagonal number theorem, we pay attention to Euler’s ideas about when we can consider a mathematical statement to be true. Finally, we discuss related results in the theory of analytic functions.

Keywords

Recurrence Relation Modular Form Formal Power Series Novi Divisor Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Authors and Affiliations

  1. 1.Department of MathematicsUniversity of TorontoTorontoCanada

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