Article
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Basic Properties of the Polygonal Sequence
Version 1
: Received: 17 February 2021 / Approved: 17 February 2021 / Online: 17 February 2021 (12:06:12 CET)
Version 2 : Received: 24 February 2021 / Approved: 24 February 2021 / Online: 24 February 2021 (10:29:09 CET)
Version 3 : Received: 25 February 2021 / Approved: 26 February 2021 / Online: 26 February 2021 (09:21:39 CET)
Version 2 : Received: 24 February 2021 / Approved: 24 February 2021 / Online: 24 February 2021 (10:29:09 CET)
Version 3 : Received: 25 February 2021 / Approved: 26 February 2021 / Online: 26 February 2021 (09:21:39 CET)
How to cite: Adegoke, K. Basic Properties of the Polygonal Sequence. Preprints 2021, 2021020385. https://doi.org/10.20944/preprints202102.0385.v3 Adegoke, K. Basic Properties of the Polygonal Sequence. Preprints 2021, 2021020385. https://doi.org/10.20944/preprints202102.0385.v3
Abstract
We study various properties of the polygonal numbers; such as their recurrence relations; fundamental identities; weighted binomial and ordinary sums; partial sums and generating functions of their powers; and a continued fraction representation for them. A feature of our results is that they are presented naturally in terms of the polygonal numbers themselves and not in terms of arbitrary integers; unlike what obtains in most literature.
Keywords
polygonal number; triangular number; summation identity; generating function; partial sum; recurrence relation
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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Commenter: Kunle Adegoke
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