restart;N := 5: Order := N:
s := series(f(z0 + dz), dz):
s0 := subs(D(f)(z0) = 0, s);eq := s0 = f(z0)*exp(u):
zet0 := solve(eq, dz);zet1 := subs(seq( (D@@k)(f)(z0) = f||k, k=0..N-1), zet0[1]):
zet2 := map(radsimp, subs(u = v^2*f2/2/f0, zet1)):
zeta := series(zet2, v);