How come the fundamental mode of Bessel's equations in solutions of the PDE in the case of the vibrations of circular membrane must be angles independent? (thus making it the axisymmetric case). So in this particular case: https://en.wikipedia.org/wiki/Vibrations_of_a_circular_membrane -> animations at the bottom of the page are indeed showing that mode $0$'s are angles independent.
I heard it is necessary for $\Theta _0$ (from separation of variables method) to be periodic, but I can't find exactly how we can see that. Is it a consequence of the initial conditions? How exactly is the link established with mode $0$?
Sincerely,