Meromorphic functions

extension of the factorial function, with its argument shifted down by 1, to real and complex numbers

analytic function

ratio of polynomial functions

function that is holomorphic everywhere except for a set of isolated points where the function may have poles

function that can be defined as the root of a polynomial equation

analytic function that does not satisfy a polynomial equation

in complex analysis, an extension of the domain of an analytic function

coefficient of the term of order −1 in the Laurent expansion of a function holomorphic outside a point, whose value can be extracted by a contour integral

pole of order zero; a point at which a holomorphic function is undefined, but it is possible to redefine the function at that point in such a way that the resulting function is regular in a neighbourhood of that point