On a Generalization of the Pentagonal Number Theorem

Ho Hon Leung

doi:10.5666/KMJ.2018.58.4.599

On a Generalization of the Pentagonal Number Theorem

Ho Hon Leung

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

We study a generalization of the classical Pentagonal Number Theorem and its applications. We derive new identities for certain infinite series, recurrence relations and convolution sums for certain restricted partitions and divisor sums. We also derive new identities for Bell polynomials.

Original language	English
Pages (from-to)	599-613
Number of pages	15
Journal	Kyungpook Mathematical Journal
Volume	58
Issue number	4
DOIs	https://doi.org/10.5666/KMJ.2018.58.4.599
Publication status	Published - 2018

Keywords

Bell polynomials
Divisor sum
Integer partition
Pentagonal number theorem
Polygonal numbers

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.5666/KMJ.2018.58.4.599

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keywords = "Bell polynomials, Divisor sum, Integer partition, Pentagonal number theorem, Polygonal numbers",

author = "Leung, {Ho Hon}",

note = "Funding Information: The author is grateful to the editor and the referees for carefully reading the paper and pointing out some mistakes in the first draft of it. Their comments were helpful to improve the quality of the article. The author is supported by UAEU Startup Grant 2016 (G00002235) from United Arab Emirates University. Publisher Copyright: {\textcopyright} Kyungpook Mathematical Journal.",

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PY - 2018

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KW - Divisor sum

KW - Integer partition

KW - Pentagonal number theorem

KW - Polygonal numbers

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On a Generalization of the Pentagonal Number Theorem

Abstract

Keywords

ASJC Scopus subject areas

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