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## Zooming in

Zooming in on the iterated exponential map…

The representation of the solution of:

$y' =\frac{y^2}{1-xy}, y(o) =1$

as a power series that has radius of convergence of $\approx 1.21$, whereas the cardioid above delimits the convergence of the solution representation defined by the implicit equation, $y =e^{xy}$ approximated by the nested/iterated exponential:

$y_0=1$

$y_n=e^{y_{n-1}x}$

The zone of convergence is larger than series representation (note the graphic represents [-2,2]x[-2,2]

Categories: Mathematica, Mathematics