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arXiv · 2401.17720

Ap\'ery Acceleration of Continued Fractions

Henri Cohen
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Abstract

We explain in detail how to accelerate continued fractions (for constants as well as for functions) using the method used by R.~Ap\'ery in his proof of the irrationality of $\zeta(3)$. 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 $\zeta(3)$, as well as a simple proof of one due to Ramanujan.

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Henri Cohen. 2024-01-31. Ap\'ery Acceleration of Continued Fractions. https://arxiv.org/abs/2401.17720

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