English: Estimating the
radius of convergence of a
power series using the
Domb–Sykes plot. As an example, the function
is analysed.
On the left, (a) is a straightforward plot of the ratio of the power-series coefficients as a function of index ; on the right, (b) is the Domb–Sykes plot of as a function of .
The green-line asymptote in the Domb–Sykes plot intercepts the vertical axis at −2 and has a slope +1. Consequently, in this example has a singularity at and slope parameter
near the singularity. And
So the limiting behaviour for large
in the Domb–Sykes plot is a
straight line, intercepting the vertical axis
at
thus providing the radius of convergence
and having a slope
from which subsequently
can be derived.