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Upper Half-Plane

UpperHalfPlane

The upper half-plane is the portion of the complex plane {x+iy:x,y in (-infty,infty)} satisfying y=I[z]>0 i.e., {x+iy:x in (-infty,infty),y in (0,infty)}. Common notations include H, H, H^+, and H (Borwein and Borwein 1987, pp. 112 and 398).

The notation H^* or H^* is sometimes used to denote H union {iinfty} union Q (Borwein and Borwein 1987, pp. 112 and 398).

See also

Complex Plane, Half-Plane, Left Half-Plane, Lower Half-Plane, Modular Function, Right Half-Plane, Upper Half-Disk

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References

Apostol, T. M. Modular Functions and Dirichlet Series in Number Theory, 2nd ed. New York: Springer-Verlag, p. 14, 1997.Borwein, J. M. and Borwein, P. B. Pi & the AGM: A Study in Analytic Number Theory and Computational Complexity. New York: Wiley, 1987.

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Upper Half-Plane

Cite this as:

Weisstein, Eric W. "Upper Half-Plane." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/UpperHalf-Plane.html

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