An function that is an analytic function except at a discrete set of points where it has singularity called "poles". At such a point, the power series expansion of the function has a finite number of terms with negative powers of z.
a function that is holomorphic almost everywhere on the complex plane , except for a set of isolated poles , which are certain well-behaved singularities
a function that is holomorphic on an open subset of the complex number plane C (or on some other connected Riemann surface ) except at points in a set of isolated poles , which are certain well-behaved singularities
a single-valued function that is analytic in all but possibly a discrete subset of its domain , and at those singularities it must go to infinity like a polynomial (i
In complex analysis, a meromorphic function on an open subset D of the complex plane is a function that is holomorphic on all D except a set of isolated points, which are poles for the function. (The terminology comes from the Ancient Greek â€œmerosâ€ (), meaning part, as opposed to â€œholosâ€ (), meaning whole.) Such functions are sometimes said to be regular functions or regular on D.