Relationship between alternating sums of powers of integers and sums of powers of integers

In this note, we consider the alternating sums of powers of integers. We write alternating sum of powers of integers as the linear combination of sums of powers of integers. As the coefficients, the special value of the Euler polynomial appears.

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Publication Details

Journal
Notes on Number Theory and Discrete Mathematics
Published
2025-11-03
DOI
https://doi.org/10.7546/nntdm.2025.31.4.761-767
Primary Topic
Advanced Mathematical Identities
Type
article
Field-Weighted Citation Impact
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article

Relationship between alternating sums of powers of integers and sums of powers of integers

Minoru Yamamoto
Notes on Number Theory and Discrete Mathematics
Advanced Mathematical Identities
article

Relationship between alternating sums of powers of integers and sums of powers of integers

Minoru Yamamoto
article en

Abstract

In this note, we consider the alternating sums of powers of integers. We write alternating sum of powers of integers as the linear combination of sums of powers of integers. As the coefficients, the special value of the Euler polynomial appears.

Notes on Number Theory and Discrete MathematicsVol. 31(4)
Openalex Percentile: Top 60%
Advanced Mathematical Identities
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Relationship between alternating sums of powers of integers and sums of powers of integers — Minoru Yamamoto · Notes on Number Theory and Discrete Mathematics (2025) | TGRS Research Map | TGRS