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) = sin x/x, since this function satisfies sinc(0) = 1.

essential singularity | pole | removable discontinuity | Riemann removable singularity theorem | singular point