An application of (iterated) Bauer-Muir acceleration can give an Ap\'ery-like continued fraction for π 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 √[3]2.
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Tomasz Stachowiak (2024) studied this question.
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