Number Theory

    

A Derivation of the Alternating Power Sum Formula

Authors: Samuel Datu Castelo

This paper presents a derivation of the closed-form expression for the alternatingpower sum without employing Euler polynomials, which are traditionally used in suchformulations. Instead, the derivation utilizes the shifted series method together withdifferentiation techniques to construct a polynomial representation for the sum. Theresulting expression is then connected to classical number-theoretic constants throughthe Riemann zeta function and Bernoulli numbers. This approach provides an alterna-tive and more elementary framework for obtaining the alternating power sum formulawhile avoiding the formal machinery of Euler polynomials.

Comments: 3 Pages.

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Submission history

[v1] 2026-03-08 22:13:18
[v2] 2026-03-12 13:29:02

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