On irrationality exponents of generalized continued fractions

TL;DR

This paper investigates how the irrationality exponent of generalized continued fractions depends on the growth rates of their partial coefficients, providing insights into their approximation properties.

Contribution

It introduces a framework linking the asymptotic irrationality exponent to the growth behavior of partial coefficients in generalized continued fractions.

Findings

Established relationships between coefficient growth and irrationality exponents.

Derived bounds for irrationality exponents based on asymptotic behaviors.

Enhanced understanding of approximation quality of generalized continued fractions.

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 $(a_n)$ and $(b_n)$.