## A little about continued fractions(This file is best viewed in a nonproportional font.) ## Definition of Continued FractionsContinued fractions have been used for an amazing variety of things, includingHomepage So what is a continued fraction? ## Sample ProgramHere is a program written in C that uses continued fractions to compute arctangents and error functions. It is a text file. It uses the forward recurrence algorithm described below. I was moved to write this program after Bob Delaney wrote a continued fraction program to compute arctangents. ## How to evaluate continued fractions
## Backward Recurrence AlgorithmThis is the more intuitive method. It consists of evaluating the expression for ## Forward recurrence AlgorithmThis method allows one to evaluate the convergents f-1, f_2 and so on recursively. ## References-
"Continued Fractions" by C. D. Olds, copyright 1963. This little book is oriented towards number theory. It can be understood by bright high school students. It's also a good introduction to continued fractions. Unfortunately, it's out of print. -
"Continued Fractions" by A. Ya. Khinchin, 3rd edition. This elegant little book, available from Dover Publications, is exclusively about simple continued fractions. -
"Die Lehre von den Kettenbruche" by Oskar Perron. Volume 1 (1954) and volume 2 (1957). In German. Apparently, this was for decades (the first edition was in 1913)*the*book in the field. This is the only one of the books here I haven't used. -
"Analytic Theory of Continued Fractions" by H. S. Wall (1948). As the title indicates, this book is about continued fractions in "analysis", rather than number theory. Thus it is about generalized continued fractions and their connections to power series, hypergeometric functions, orthogonal polynomials, infinite matrices, Pade approximants, definite integrals, and so on. It was reprinted in 2000 by the American Mathematical Society. -
"Continued Fractions Analytical Theory and Applications (volume 11 of Encyclopedia of Mathematics and Its Applications)" by William B. Jones, copyright 1980. This is a tome. Unfortunately, it also is out of print. Despite its length, it is not completely self-contained; for example it uses results from the book by Wall. -
"Continued Fractions Volume 1: Convergence Theory", 2nd edition, 2008, by Lisa Lorentzen and Haakon Waadeland. Aimed at readers "in or near mathematics". -
"Continued Fractions" article in Eric's World of Mathematics
christopher e reed at cs . com> This page was created on June 9, 2002. It was changed/fiddled with on October 23, 2010. Homepage |