Asymptotic Behavior of Entire Functions with Exceptional Values in the Borel Relation

  • P. V. Filevych


Let M f(r) and μ f (r) be, respectively, the maximum of the modulus and the maximum term of an entire function f and let l(r) be a continuously differentiable function convex with respect to ln r. We establish that, in order that ln M f(r) ∼ ln μ f (r), r → +∞, for every entire function f such that μ f (r) ∼ l(r), r → +∞, it is necessary and sufficient that ln (rl′(r)) = o(l(r)), r → +∞.
How to Cite
Filevych, P. V. “Asymptotic Behavior of Entire Functions With Exceptional Values in the Borel Relation”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 53, no. 4, Apr. 2001, pp. 522-30,
Research articles