Euler's Continued Fraction

Author

Eric W. Weisstein
August 3, 2008

This notebook downloaded from http://mathworld.wolfram.com/notebooks/NumberTheory/EulersContinuedFraction.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/EulersContinuedFraction.html.

©2008 Wolfram Research, Inc. except for portions noted otherwise

Identity

x/(1+ContinuedFractionK[(2n-1)^2 x^2,2n+1-(2n-1)x^2,{n,∞}])

N[{ArcTan[x],x/(1+ContinuedFractionK[(2n-1)^2 x^2,2n+1-(2n-1)x^2,{n,10}])}/.x->1/10,20]