SINGULARITY

also called singular point in mathematical analysis, point of the complex plane (that is, a complex number of the form z0 = x0 + iy0) at which some function of the complex variable z is not analytic (that is, the function cannot be expressed as an infinite series in powers of z). At points arbitrarily close to the singularity, the function is analytic. For example, the function f (z) = ez/z is analytic throughout the complex planefor all values of zexcept at the point z = 0, where the series expansion is not defined because it contains the term 1/z. The series is 1/z + 1 + z/2 + z2/6 + . . . +zn/(n + 1)! + . . . .