9.2: Holomorphic and Meromorphic Functions
- Page ID
- 6523
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- A function that is analytic on a region \(A\) is called holomorphic on \(A\).
- A function that is analytic on \(A\) except for a set of poles of finite order is called meromorphic on \(A\).
Let
\[f(z) = \dfrac{z + z^2 + z^3}{(z - 2)(z - 3)(z - 4)(z - 5)}. \nonumber \]
This is meromorphic on \(C\) with (simple) poles at \(z = 2, 3, 4, 5.\)