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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.06312 |
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| _version_ | 1866916782657241088 |
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| author | Cimpoeas, Mircea |
| author_facet | Cimpoeas, Mircea |
| contents | We present a new combinatorial approach to the computation of the (real) Fourier expansions of $\cos^n(t)$ and $\sin^n(t)$, where $n\geq 1$ is an integer. As an application, we compute the Fourier expansions of $f(t)=\frac{1}{a-\cos t}$ and $g(t)=\frac{1}{a-\sin t}$, where $a\in\mathbb R$ with $|a|>1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_06312 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A combinatorial approach to the Fourier expansions of powers of cos and sin Cimpoeas, Mircea General Mathematics 05A19, 26A09, 42A20 We present a new combinatorial approach to the computation of the (real) Fourier expansions of $\cos^n(t)$ and $\sin^n(t)$, where $n\geq 1$ is an integer. As an application, we compute the Fourier expansions of $f(t)=\frac{1}{a-\cos t}$ and $g(t)=\frac{1}{a-\sin t}$, where $a\in\mathbb R$ with $|a|>1$. |
| title | A combinatorial approach to the Fourier expansions of powers of cos and sin |
| topic | General Mathematics 05A19, 26A09, 42A20 |
| url | https://arxiv.org/abs/2506.06312 |