Generalization of the fricke theorem on entire functions of finite index - Sheremeta, M. M. (Ukrains’kyi Matematychnyi Zhurnal, 1996)
We prove that, for every sequence (a k) of complex numbers satisfying the conditions Σ(1/|a k |) < ∞ and |a k+1| − |a k | ↗ ∞ (k → ∞), there exists a continuous functionl decreasing to 0 on [0, + ∞] and such that f(z) = Π(1 −z/|a k |) is an entire function of finite l-index.