IsMeromorphic

Input: IsMeromorphic(f(z), For(z, c))
$$f(z) \text{ is meromorphic at } z = c$$

Represents the predicate that $f(z)$ is meromorphic in some open neighborhood of the point $c$.

Input: IsMeromorphic(f(z), ForElement(z, S))
$$f(z) \text{ is meromorphic on } z \in S$$

Represents the predicate that $f(z)$ is meromorphic in some open neighborhood of every point in the set $S$.

Input: IsMeromorphic(f(z), For(z, UnsignedInfinity))
$$f(z) \text{ is meromorphic at } z = {\tilde \infty}$$

Represents the predicate that $f\!\left(\frac{1}{z}\right)$ is meromorphic at 0.

Input: IsMeromorphic(f(z), For(z, ConstI*Infinity))
$$f(z) \text{ is meromorphic at } z = i \infty$$

Represents the predicate that $f(z)$ is a periodic function on the upper half plane that is meromorphic at infinity (in the sense of modular function theory).

Last updated: 2020-03-06 00:22:16