STRONG UNBOUNDEDNESS OF UNBOUNDED ANALYTIC-FUNCTIONS

It is proved that if f is an unbounded analytic function in the open unit disc D, then there must exist a sequence (z(n)) in D such that for every j = 0, 1, 2,..., f((j))(z(n)) --> infinity as n --> infinity. This answers affirmatively a question asked by J. Langley and L. Rubel in 1984.