In my second paper, we'd seen how to create formulae for the sum of the terms
of a generalized harmonic progression with integer parameters, that is,
$\sum_{j}1/(a j+b)^k$, where $a$ and $b$ are integers. Those formulae were more
general than the ones we came up with for the harmonic numbers in the first
paper. In this new paper we will make these formulae even more general by
removing the restriction that $a$ and $b$ be integers, that is, here we'll
address $\sum_{j}1/(a\text{i} j+b)^k$, where $a$ and $b$ are any complex
numbers and $\text{i}$ is the imaginary unity. These new, relatively simple
formulae always hold, except when $\text{i} b/a\in \mathbb{Z}$. This paper
employs a slightly modified version of the reasoning used in the previous
paper, which has already been fully explained in previous papers. Nonetheless,
we will make another brief exposition of the principle used to derive such
formulae.