On irrationality exponents of generalized continued fractions

preprint2014arXivOpen access

Abstract

We study how the asymptotic irrationality exponent of a given generalized continued fraction \[ \K_{n=1}^\infty \frac{a_n}{b_n}\,,\quad a_n, b_n\in \mathbb{Z}^+, \] behaves as a function of growth properties of partial coefficient sequences (an)(a_n) and (bn)(b_n).

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