A convergence theorem for continued fractions of the form $K_{n=1}^{\infty} a_{n}/1$

James Mc Laughlin; Nancy J. Wyshinski

doi:10.1016/j.cam.2004.09.055

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arXiv · 1812.11205

A convergence theorem for continued fractions of the form $K_{n=1}^{\infty} a_{n}/1$

James Mc Laughlin·Nancy J. Wyshinski

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Abstract

In this paper we present a convergence theorem for continued fractions of the form $K_{n=1}^{\infty}a_{n}/1$. By deriving conditions on the $a_{n}$ which ensure that the odd and even parts of $K_{n=1}^{\infty}a_{n}/1$ converge, these same conditions also ensure that they converge to the same limit. Examples will be given.

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James Mc Laughlin, Nancy J. Wyshinski. 2018-12-28. A convergence theorem for continued fractions of the form $K_{n=1}^{\infty} a_{n}/1$. https://doi.org/10.1016/j.cam.2004.09.055

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