Irrational Acceleration of a Continued Fraction of $\pi$

Tomasz Stachowiak

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arXiv · 2406.01295

Irrational Acceleration of a Continued Fraction of $\pi$

Tomasz Stachowiak

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Abstract

An application of (iterated) Bauer-Muir acceleration can give an Ap\'ery-like continued fraction for $\pi$ with irrational coefficients, and much faster convergence. It can be considered a generalized continued fraction with the same matrix representation as the standard case, but the dimension increased due to irrationality. The construction is also given for $\ln(2)$ and $\sqrt[3]{2}$.

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Tomasz Stachowiak. 2024-06-03. Irrational Acceleration of a Continued Fraction of $\pi$. https://arxiv.org/abs/2406.01295

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