Removable Singularity

A removable singularity is a singular point z_0 of a function f(z) for which it is possible to assign a complex number in such a way that f(z) becomes analytic. A more precise way of defining a removable singularity is as a singularity z_0 of a function f(z) about which the function f(z) is bounded. For example, the point x_0=0 is a removable singularity in the sinc function sinc(x)=sinx/x, since this function satisfies sinc(0)=1.

See also

Essential Singularity, Pole, Removable Discontinuity, Riemann Removable Singularity Theorem, Singular Point

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Krantz, S. G. "Removable Singularities, Poles, and Essential Singularities." §4.1.4 in Handbook of Complex Variables. Boston, MA: Birkhäuser, p. 42, 1999.

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Removable Singularity

Cite this as:

Weisstein, Eric W. "Removable Singularity." From MathWorld--A Wolfram Web Resource.

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