Polynomial Identities for Binomial Sums of Harmonic Numbers of Higher Order

Takao Komatsu () and B. Sury
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Takao Komatsu: Faculty of Education, Nagasaki University, Nagasaki 852-8521, Japan
B. Sury: Stat-Math Unit, Indian Statistical Institute, 8th Mile Mysore Road, Bangalore 560059, India

Mathematics, 2025, vol. 13, issue 2, 1-12

Abstract: We study the formulas for binomial sums of harmonic numbers of higher order ∑ k = 0 n H k ( r ) n k ( 1 − q ) k q n − k = H n ( r ) − ∑ j = 1 n D r ( n , j ) q j j . Recently, Mneimneh proved that D 1 ( n , j ) = 1 . In this paper, we find several different expressions of D r ( n , j ) for r ≥ 1 .

Keywords: polynomial identities; harmonic numbers; determinant; Bell polynomials (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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