“Cauchy's formula for derivatives”的概念、定义、习题解题方法及翻译-数学辞典

单词

Cauchy's formula for derivatives

释义

Cauchy's formula for derivatives

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

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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