Number Theory

   

Generalized Harmonic Progression

Authors: Jose R. Sousa

This paper presents formulae for the sum of the terms of a harmonic progression of order $k$ with integer parameters, more precisely, $\sum_{j=1}^{n}1/(a j+b)^k$, and for the partial sums of two Fourier series associated with them, denoted here by $C^m_{k}(a,b,n)$ and $S^m_{k}(a,b,n)$ (here, the term $``$harmonic progression$"$ is used loosely, as for some parameter choices, $a$ and $b$, the result may not be a harmonic progression). We provide a generalization of the formulae we created in $\textit{Generalized Harmonic Numbers Revisited}$, which was achieved by using an extension of the reasoning employed before.

Comments: 8 Pages.

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Submission history

[v1] 2019-07-29 22:10:51

Unique-IP document downloads: 8 times

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