Number Theory

    

Generalized Harmonic Progressions

Authors: Jose Risomar Sousa

This paper presents formulae for the sum of the terms of a harmonic progression of order k with integer parameters, HPu2096(n), and for the partial sums of its two associated Fourier series, Cᶻu2096(a, b, n) and Sᶻu2096(a, b, n). HPu2096(n) is built from the ground up, with a power series for 1/(aj + b)ᵏ that is summed over j using Faulhaber's formula. These new formulae are a generalization of the formulae created in a previous paper and were achieved using a slightly modified version of the reasoning employed before.

Comments: 10 Pages.

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[v1] 2026-09-27 21:49:33

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