ABSTRACT
This convergent expansion is also an asymptotic expansion (Theorem 3.1), and since the asymptotic expansion of f(z) is unique it follows that as = 6,. This completes the proof. 7.6 The final result in this section is immediately derivable from Theorem 7.2: Theorem 7.3 Letf(z) be single valued and holomorphic in a deleted neighborhood of infnity. Assume that (7.06) holds in a closed sector S, and also that this expansion diverges for all finite z. Then the angle of S is less than 2n and f (z) has an essential singularity at infnity.
