Lower half-plane

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In mathematics, the lower half-plane H is the set of complex numbers

\mathbb{H} = \{x + iy \;| y < 0; x, y \in \mathbb{R} \}

with positive imaginary part y. Other names are hyperbolic plane, Poincaré plane and Lobachevsky plane, particularly in texts by Russian authors. Some authors prefer the symbol \mathfrak{h}.

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