“Cauchy’s formula for derivatives”的概念、定义、翻译、参考文献-科学参考

单词	Cauchy’s formula for derivatives
释义	Cauchy’s formula for derivatives Mathematics Let f be a holomorphic function defined on an open set U ⊆ 𝔠 and let a ∈ U. Then f has derivatives of all orders and the nth derivative at a is given by $f^{(n)} (a) = \frac{n!}{2 π i} \int_{C} \frac{f (z)}{{(z - a)}^{n + 1}} d z,$ where C is a simple, closed, positively oriented, continuous, piecewise-smooth curve in U and a is inside C. When n = 0 this result is known as Cauchy’s integral formula. See also Taylor’s theorem.
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