A Jentzsch-Theorem for Kapteyn, Neumann and General Dirichlet Series

@article{Bornemann2022AJF,
  title={A Jentzsch-Theorem for Kapteyn, Neumann and General Dirichlet Series},
  author={Folkmar A. Bornemann},
  journal={Computational Methods and Function Theory},
  year={2022}
}
  • F. Bornemann
  • Published 15 July 2021
  • Mathematics
  • Computational Methods and Function Theory
Comparing phase plots of truncated series solutions of Kepler’s equation by Lagrange’s power series with those by Bessel’s Kapteyn series strongly suggests that a Jentzsch-type theorem holds true not only for the former but also for the latter series: each point of the boundary of the domain of convergence in the complex plane is a cluster point of zeros of sections of the series. We prove this result by studying properties of the growth function of a sequence of entire functions. For series… 

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