Parameterized Finite Binomial Sums

Necdet Batır and Junesang Choi ()
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Necdet Batır: Department of Mathematics, Nevşehir Haci Bektaş Veli University, Nevşehir 50300, Turkey
Junesang Choi: Department of Mathematics, Dongguk University, Gyeongju 38066, Republic of Korea

Mathematics, 2024, vol. 12, issue 16, 1-20

Abstract: We offer intriguing new insights into parameterized finite binomial sums, revealing elegant identities such as ∑ k = 0 , k ≠ n m + n ( − 1 ) k n − k m + n k = ( − 1 ) n m + n n ( H m − H n ) , where n , m are non-negative integers and H n is the harmonic number. These formulas beautifully capture the intricate relationship between harmonic numbers and binomial coefficients, providing a fresh and captivating perspective on combinatorial sums.

Keywords: binomial sums; parameterized sums; harmonic sums; gamma function; polygamma function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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