Generalized Harmonic Progression

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