1. (of a complex function) analytic everywhere in a region except at isolated points where it has poles.
Usage: mathematics; complex analysis

Examples

• The tangent function is a meromorphic function on the complex plane.
• A meromorphic function can be expressed as the ratio of two analytic functions.
• In complex analysis, meromorphic functions generalize analytic functions by allowing poles.
• The Riemann zeta function is meromorphic with a single pole at s = 1.
• Meromorphic functions are important tools for solving differential equations in mathematics.