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arXiv · 1811.11305

Generalized Harmonic Progression

Jose Risomar Sousa
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Abstract

This paper presents formulae for the sum of the terms of a harmonic progression of order $k$ with integer parameters, $\mathrm{HP}_k(n)$, and for the partial sums of its two associated Fourier series, $C^z_{k}(a,b,n)$ and $S^z_{k}(a,b,n)$. $\mathrm{HP}_k(n)$ 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.

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Jose Risomar Sousa. 2018-11-27. Generalized Harmonic Progression. https://arxiv.org/abs/1811.11305

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