Definition:Holomorphic Complex Function/Also known as

Holomorphic Function: Also known as

Some authors refer to a holomorphic function on an open set $U$ of $\C$ as an analytic (complex) function.

This is because, by Holomorphic Function is Analytic, they are equivalent.

We also say that $f$ is complex-differentiable in $U$.

Sometimes the term regular function can be seen, which means the same thing.

Sources

• 1964: Murray R. Spiegel: Theory and Problems of Complex Variables ... (previous): Chapter $3$: Complex Differentiation and The Cauchy-Riemann Equations: Analytic Functions
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): holomorphic
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): holomorphic function
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): holomorphic function
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): holomorphic
• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): holomorphic
• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): regular function