We study how the asymptotic irrationality exponent of a given generalized continued fraction ∞

We give explicit and asymptotic lower bounds for the quantity |e s/t −M/N| by studying a generalized continued fraction expansion of e s/t . In cases |s| ≥ 3 we improve existing results by extracting a large common factor from the numerators and the denominators of the convergents of that generalized continued fraction.

We study generalized continued fraction expansions of the formwhere N is a fixed positive integer and the partial numerators ai are positive integers for all i. We call these expansions dnN expansions and show that every positive real number has infinitely many dnN expansions for each N . In particular we study the dnN expansions of rational numbers and quadratic irrationals. Finally we show that every positive real number has for each N a dnN expansion with bounded partial numerators.

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