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Irrational Acceleration of a Continued Fraction of $\pi$
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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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Continued Fractions of Polynomial Type: Theory and Encyclopedic Dictionary
A theory-plus-dictionary of polynomial-type continued fractions with explicit convergence rates and Apéry-style accelerations, mostly new or newly quantified.
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