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arXiv.org e-Print Archive
Preprint . 2021
Data sources: arXiv.org e-Print Archive
Rocky Mountain Journal of Mathematics
Article . 2025 . Peer-reviewed
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https://dx.doi.org/10.48550/ar...
Article . 2021
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REPRESENTATIONS BY ORDERED BELL AND DEGENERATE ORDERED BELL POLYNOMIALS

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Apr 2025Embargo end date: 01 Jan 2021Publisher:Rocky Mountain Mathematics ConsortiumJournal:Rocky Mountain Journal of Mathematics, volume 55 (issn: 0035-7596, Copyright policy )
Authors: Kim, Dae san; Kim, Taekyun;

doi: 10.1216/rmj.2025.55.381 , 10.48550/arxiv.2110.03178

arXiv: http://arxiv.org/abs/2110.03178

REPRESENTATIONS BY ORDERED BELL AND DEGENERATE ORDERED BELL POLYNOMIALS

Abstract

In this paper, we consider the problem of representing any polynomial in terms of the ordered Bell and degenerate ordered Bell polynomials, and more generally of the higher-order ordered Bell and higher-order degenerate ordered Bell polynomials. We derive explicit formulas with the help of umbral calculus and illustrate our results with some examples.

20 pages. arXiv admin note: substantial text overlap with arXiv:2108.05049, arXiv:2109.13700

Keywords

Mathematics - Number Theory, FOS: Mathematics, Number Theory (math.NT), 05A19, 05A40, 11B68, 11B83

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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