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image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao https://doi.org/10.1...arrow_drop_down
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
https://doi.org/10.1007/bfb006...
Part of book or chapter of book . 1974 . Peer-reviewed
License: Springer TDM
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A formula relevant to functions meromorphic in an angle and its applications

Authors: W. H. J. Fuchs;

A formula relevant to functions meromorphic in an angle and its applications

Abstract

I. The formula referred to in the title is (I) below. The usefulness of the formula is based on the fact that it relates the value of a meromorphic function f(z) at a point of a sector to integrals of log If(z) I over arcs in this sector. Since such integrals are very directly related to the quantities considered in the Nevanlinna theory, the formula is easier to use than the usual Green's function formula for functions meromorphie in a sector which involves integrals of log Ifl along the boundary of the sector. An essentially equivalent formula was used by V. P. Petrenko in his proof of Paley's Conjecture [3]. By casting out some terms that were negligible for his purpose Petrenko actually complicated his proof, the complete formula (I) can be proved quite simply. Petrenko's Formula. Let f(z) b emeromorphic i_~n

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popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
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influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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impulse
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