Generalized Harmonic Progression

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, $C_k^z(a,b,n)$ and $S_k^z(a,b,n)$. ${\mathrm{HP}}_k(n)$ 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.

Improved the writing, set the grammar to academic standards and numbered some formulas