Apéry Acceleration of Continued Fractions
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911768354226176 |
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| author | Cohen, Henri |
| author_facet | Cohen, Henri |
| contents | We explain in detail how to accelerate continued fractions (for constants as well as for functions) using the method used by R.~Apéry in his proof of the irrationality of $ζ(3)$. We show in particular that this can be applied to a large number of continued fractions which can be found in the literature, thus providing a large number of new continued fractions. As examples, we give a new continued fraction for $\log(2)$ and for $ζ(3)$, as well as a simple proof of one due to Ramanujan. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_17720 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Apéry Acceleration of Continued Fractions Cohen, Henri Number Theory Complex Variables We explain in detail how to accelerate continued fractions (for constants as well as for functions) using the method used by R.~Apéry in his proof of the irrationality of $ζ(3)$. We show in particular that this can be applied to a large number of continued fractions which can be found in the literature, thus providing a large number of new continued fractions. As examples, we give a new continued fraction for $\log(2)$ and for $ζ(3)$, as well as a simple proof of one due to Ramanujan. |
| title | Apéry Acceleration of Continued Fractions |
| topic | Number Theory Complex Variables |
| url | https://arxiv.org/abs/2401.17720 |