using sinh(x) ?

[sheldonison]

hmm

wouldnt by that logic almost every superfunction be periodic ??

i mean => af = f ' (0) * f(x)

lim n-> oo af^[n] ( a^(z-n) )

real(z) << -10

since a^z is periodic in direction Q , with period i*2pi/ln(a) , then the superfunction of af is also periodic with that period.

Mostly correct, with period i*2pi/ln(a). But not true for every superfunction. Knesser's solution for sexp_e is not periodic, but is pseudo periodic. It starts with the superfunction, which is complex valued at the real axis, and then does a conformal mapping, to put real values back on the real axis, along with a Schwarz reflection. For i(z)>=1i, sexp_e is fairly close to the (linearly shifted) complex valued superfunction. You can see the complex pseudo periodicity in the contour graphs in Kouznetsov's paper on the sexp_e.
- Sheldon