On Some Binomial Coefficient Identities with Applications
Necdet Batır, Sezer Sorgun, and Sevda Atpınar
Department of Mathematics
Nevşehir Hacı Bektaş Veli University
In this paper, we present an alternative proof for a generalization of a
binomial identity by Simons, initially proven by Munarini. Unlike previous
proofs, our approach uses the Taylor theorem and the Wilf-Zeilberger
algorithm. We also offer a new binomial sum identity and generalize a
combinatorial identity by Alzer and Kouba. Additionally, we derive several
harmonic number identities, including the proof for
Hn and a formula
involving the square of binomial coefficients and harmonic numbers.
Full version: pdf,
Received January 10 2023; revised versions received January 13 2023; January 16 2023; April 17 2023.
Published in Journal of Integer Sequences,
April 18 2023.
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