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词汇 Conjugate function
分类 英语词汇 英语翻译词典
释义

Conjugate function

英语百科

Harmonic conjugate

(重定向自Conjugate function)

In mathematics, a function u(x,\,y) defined on some open domain \Omega\subset\R^2 is said to have as a conjugate a function v(x,\,y) if and only if they are respectively real and imaginary parts of a holomorphic function  f(z) of the complex variable z:=x+iy\in\Omega. That is, v is conjugate to u if f(z):=u(x,y)+iv(x,y) is holomorphic on \Omega. As a first consequence of the definition, they are both harmonic real-valued functions on \Omega. Moreover, the conjugate of u, if it exists, is unique up to an additive constant. Also, u is conjugate to v if and only if v is conjugate to -u.

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