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In mathematics, in the field of complex analysis, a Nevanlinna function is a complex function which is an analytic function on the open upper half-plane H {\displaystyle \,{\mathcal {H}}\,} and has non-negative imaginary part. A Nevanlinna function maps the upper half-plane to itself or to a real constant, but is not necessarily injective or surjective. Functions with this property are sometimes also known as Herglotz, Pick or R functions.
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