# Sequences of analytic functions and their zeros

@article{Ganelius1954SequencesOA,
title={Sequences of analytic functions and their zeros},
author={Tord H. Ganelius},
journal={Arkiv f{\"o}r Matematik},
year={1954},
volume={3},
pages={1-50}
}
• T. Ganelius
• Published 1 March 1954
• Philosophy
• Arkiv för Matematik

### On the distribution of roots of polynomials in sectors. I

where an, ao E C*. P. Bloch and G. P61ya, E. Schmidt, and, finally, I. Schur [13] estimated the number of real roots of P in terms of its length L(P) , degree n, and the absolute value of the product

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

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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

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### THE SHARP ERDŐS-TURÁN INEQUALITY

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## References

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### A further note on trigonometrical inequalities

• A. Ingham
• Mathematics
Mathematical Proceedings of the Cambridge Philosophical Society
• 1950
1. The aim of this note is to prove the Theorem. Let where the λnare real and and let Then A similar result holds for infinite seriesconverging uniformly in [−T, T].

### Sur les fonctions entières

© Bulletin de la S. M. F., 1883, tous droits réservés. L’accès aux archives de la revue « Bulletin de la S. M. F. » (http://smf. emath.fr/Publications/Bulletin/Presentation.html) implique l’accord

### On sequences of polynomials and the distribution of their zeros

THEOREM 2. If the sequence (1) converges uniformly in a circle \z\ <R, and if the roots znv lie in the half-plane %z^0 for each n, then the sequence (1) converges uniformly in every finite domain to