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arXiv · 1702.07457

Continued fractions of certain Mahler functions

Dmitry Badziahin
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Abstract

We investigate the continued fraction expansion of the infinite products $g(x) = x^{-1}\prod_{t=0}^\infty P(x^{-d^t})$ where polynomials $P(x)$ satisfy $P(0)=1$ and $\deg(P) 1$ such that $g(b)\neq0$ the irrationality exponent of $g(b)$ equals two. In the case $d=3$ we provide a partial analogue of the last result with several collections of polynomials $P(x)$ giving the irrationality exponent of $g(b)$ strictly bigger than two.

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Dmitry Badziahin. 2017-02-24. Continued fractions of certain Mahler functions. https://arxiv.org/abs/1702.07457

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