Meromorphic functions are complex functions that are holomorphic (analytic) on an open set except for a set of isolated poles, where they exhibit a specific type of singularity. They can be viewed as the combination of holomorphic functions and poles, which are points where the function approaches infinity. This unique property allows meromorphic functions to be expressed in terms of rational functions and connects deeply with various aspects of complex analysis, including differential equations and the theory of residues.
congrats on reading the definition of meromorphic functions. now let's actually learn it.