Geodesic
On Koenig's theorem for integer functions of finite order
Numerical methods and programming, Tome 21 (2020) no. 3, pp. 280-289.

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It is shown that Koenig's theorem on zeros of analytic functions applied to the logarithmic derivative of an integer function of finite order leads to an algorithm of finding zeros whose convergence domains are the Voronoi polygons of the zeros to be found. Since the Voronoi diagram of a sequence of zeros is a set of measure zero, this algorithm is globally convergent. The rate of convergence is estimated. For higher-order iterations that are constructed using Koenig's theorem, the effect of root multiplicity on the convergence domain is considered and the convergence rate is estimated for this case.
Keywords: logarithmic derivative; higher-order derivative; simplest fractions; convergence radius of power series; Voronoi polygons (cells); global convergence. 
@article{VMP_2020_21_3_a6,
     author = {A. N. Gromov},
     title = {On {Koenig's} theorem for integer functions of finite order},
     journal = {Numerical methods and programming},
     pages = {280--289},
     publisher = {mathdoc},
     volume = {21},
     number = {3},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2020_21_3_a6/}
}
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A. N. Gromov. On Koenig's theorem for integer functions of finite order. Numerical methods and programming, Tome 21 (2020) no. 3, pp. 280-289. http://geodesic.mathdoc.fr/item/VMP_2020_21_3_a6/