Abstract
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 thatf(z) = Π(1 −z/|a k |) is an entire function of finitel-index.
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References
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M. N. Sheremeta and A. D. Kuzyk, “On the logarithmic derivative and zeros of an entire function of finitel-index,”Sib. Mat. Zh.,33, No. 2, 142–150 (1992).
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Sheremeta, M.M. Generalization of the fricke theorem on entire functions of finite index. Ukr Math J 48, 460–466 (1996). https://doi.org/10.1007/BF02378535
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DOI: https://doi.org/10.1007/BF02378535