Generalized Harmonic Progression Part II

Abstract

In a previous paper, we saw how to create formulae for the sum of the terms of a harmonic progression of order $k$, ${\mathrm{HP}}_k(n)$, with integer parameters, $a$ and $b$. In this new paper we make those formulae even more general by lifting the restriction that the parameters be integers. The new formula holds always, except when $ib/a\in \mathbb{Z}$. Here a slightly modified version of the reasoning used before is introduced, in a standalone exposition that does not require prior knowledge of the precursor paper. A notable advantage of this new approach is that it can be used to find summation formulae for the reciprocal of polynomials, that is, ${\sum }_{j}1/p(j)$.

arXiv commentImproved the writing and emphasized an important feature of the new formula