johanschott / pade_approximants Goto Github PK

I have tried to use the Pade approximation for the arctan(x) function as it resembles a Green's function in condensed matter physics. However, by using its function values on the real axis as an input for the Pade approximation and then trying to find the function values on the imaginary axis I ran into some issues. The arctan(i*x) shows step-like behavior which can be easily observed since it is an analytical function. On the other hand, using the Pade approximation results in large fluctuations at the edges (see plot below).

For simplicity, the plot only includes the real part of both, the analytical function arctan(i*x) and the Pade approximation of arctan(x) on the imaginary axis.

I was wondering whether your code can find the analytical continuation of the Arctan(x) from the real axis to the imaginary axis more accurately than my code.