Generalized Harmonic Progression
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2018
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| _version_ | 1866911665048518656 |
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| author | Sousa, Jose Risomar |
| author_facet | Sousa, Jose Risomar |
| contents | 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, $C^z_{k}(a,b,n)$ and $S^z_{k}(a,b,n)$. $\mathrm{HP}_k(n)$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1811_11305 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Generalized Harmonic Progression Sousa, Jose Risomar Number Theory 11-XX 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, $C^z_{k}(a,b,n)$ and $S^z_{k}(a,b,n)$. $\mathrm{HP}_k(n)$ 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. |
| title | Generalized Harmonic Progression |
| topic | Number Theory 11-XX |
| url | https://arxiv.org/abs/1811.11305 |