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Riemann Removable Singularity Theorem


Let f:D(z_0,r)\{z_0}->C be analytic and bounded on a punctured open disk D(z_0,r), then lim_(z->z_0)f(z) exists, and the function defined by f^~:D(z_0,r)->C

 f^~(z)={f(z)   for z!=z_0; lim_(z^'->z_0)f(z^')   for z=z_0
(1)

is analytic.


See also

Removable Singularity

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References

Krantz, S. G. "The Riemann Removable Singularity Theorem." §4.1.5 in Handbook of Complex Variables. Boston, MA: Birkhäuser, pp. 42-43, 1999.

Referenced on Wolfram|Alpha

Riemann Removable Singularity Theorem

Cite this as:

Weisstein, Eric W. "Riemann Removable Singularity Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/RiemannRemovableSingularityTheorem.html

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