 Order of a zero of a holomorphic function

ID: order-of-a-zero-of-a-holomorphic-function

Codex  0 Created 2026-09-24 Updated 2026-10-03

If a nonzero holomorphic function has expansion

f (z) = (z - z_{0})^{m} g (z), g (z_{0}) \neq = 0,

then

m

is the order or multiplicity of its zero at

z_{0}

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