CPE / 'P' is different from definition inside "impedance.py" about equivalentcircuits.jl HOT 5 CLOSED

Here is my proposal for the part in:
function circuitfunction(Circuit)
original:

replace(Circuit,match=>"T*(2*π*f)^(-N)"*"*(cos((π*N)*0.5)-sin((π*T)*0.5)im)")

new:

replace(Circuit,match=>"(1/(T*(2im*π*f)^N))")

from equivalentcircuits.jl.

Unfortunately, there is a lack of standard definitions of Warburg and CPE elements in the literature. There are two different definitions for CPEs in common use, the one derived by Boukamp and the one in Barsoukov and Mcdonald's popular textbook.

For previous work reviewing and comparing equivalent circuits, I have implemented all definitions. They have the same modeling capacity, but if you want to conveniently compare specific parameters to those using a particular definition, I can provide an option for that. I appreciate all your feedback and will be looking into all your suggestions and questions in December.

from equivalentcircuits.jl.

unfortunately, there is a deviation between impedance.py and EquivalentSircuits.jl for more complicated EC.
For a simple one like "[C1,P2]" there is a perfect match, but for more complicated one like: "[C1-P2,[R3,C4-L5-P6]]",
there is a difference in the simulation.
Please have a look on my script to compare both packages:
debug_EquivalentCircuit_Impedance_Simulation.jl

from equivalentcircuits.jl.

I have set up a simple script for the simulation of the equivalent circuit: "[C1-P2,R3]"
The results of three different ways are compared:
example_simple_EquivCirc_including_constant_phase.jl

from equivalentcircuits.jl.

Here is a link regarding the two different approaches:
http://www.consultrsr.net/resources/eis/zarc.htm

from equivalentcircuits.jl.