Euler's Continued Fraction Formula

In the analytic theory of continued fractions, Euler's continued fraction formula is an identity connecting a very general infinite series to an infinite continued fraction. First published in 1748, it was originally understood as a simple identity linking a finite sum to a finite continued fraction, with the extension to the infinite case seen as immediately apparent; it is now valued as a tool in analytic work on the general convergence problem for infinite continued fractions with complex terms. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/