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

paper

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

arXiv:1812.11205 · doi:10.1016/j.cam.2004.09.055

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.

8 pages

A convergence theorem for continued fractions of the form Kn=1∞​an​/1

Abstract

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