Combinatorial Identities with Multiple Harmonic-like Numbers

Multiple harmonic-like numbers are studied using the generating function approach. A closed form is stated for binomial sums involving these numbers and two additional parameters. Several corollaries and examples are presented which are immediate consequences of the main result. Finally, combinatori...

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Bibliographic Details
Published in:AppliedMath 2024-09, Vol.4 (3), p.986-998
Main Authors: Adegoke, Kunle, Frontczak, Robert
Format: Article
Language:English
Subjects:
binomial transform
harmonic number
multiple harmonic-like numbers
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Summary:Multiple harmonic-like numbers are studied using the generating function approach. A closed form is stated for binomial sums involving these numbers and two additional parameters. Several corollaries and examples are presented which are immediate consequences of the main result. Finally, combinatorial identities involving harmonic-like numbers and other prominent sequences like hyperharmonic numbers and odd harmonic numbers are offered.
ISSN:2673-9909
2673-9909
DOI:10.3390/appliedmath4030053