On irrationality exponents of generalized continued fractions

Jaroslav Hancl; Kalle Lepp\"al\"a; Tapani Matala-aho; Topi T\"orm\"a

arxiv: 1409.1511 · v1 · pith:VK6CIHLOnew · submitted 2014-09-04 · 🧮 math.NT

On irrationality exponents of generalized continued fractions

Jaroslav Hancl , Kalle Lepp\"al\"a , Tapani Matala-aho , Topi T\"orm\"a This is my paper

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keywords continuedgeneralizedirrationalityasymptoticbehavescoefficientexponentexponents

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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 $(b_n)$.

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On irrationality exponents of generalized continued fractions

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