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Local degree of a holomorphic map ( $m_{f} (p)$ )

If a nonconstant holomorphic map has local-coordinate expression

f (z) - f (p) = a (z - p)^{m} + O ((z - p)^{m + 1}), a \neq = 0,

then

m = m_{f} (p)

is its local degree, multiplicity, or ramification index at

p

.

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Solution