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In mathematics, a real-valued function defined on a connected open set is said to have a conjugate (function) if and only if they are respectively the real and imaginary parts of a holomorphic function of the complex variable That is, is conjugate to if is holomorphic on As a first consequence of the definition, they are both harmonic real-valued functions on . Moreover, the conjugate of if it exists, is unique up to an additive constant. Also, is conjugate to if and only if is conjugate to .

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  • En matemáticas, se dice que una función de variables reales definida en un conjunto abierto conexo tiene una función conjugada si y sólo si son respectivamente las partes reales e imaginarias de un función holomorfa de variable compleja Es decir, es conjugada de si y solo si es holomorfa en . Como primera consecuencia de la definición, ambas funciones son armónicas en . Además, si existe la conjugada de esta es única salvo una constante aditiva. (es)
  • In mathematics, a real-valued function defined on a connected open set is said to have a conjugate (function) if and only if they are respectively the real and imaginary parts of a holomorphic function of the complex variable That is, is conjugate to if is holomorphic on As a first consequence of the definition, they are both harmonic real-valued functions on . Moreover, the conjugate of if it exists, is unique up to an additive constant. Also, is conjugate to if and only if is conjugate to . (en)
  • 在數學中,調和共軛(Harmonic conjugate)是針對函數的概念。定義在開集中的函數,另一個函數為其共軛函數的充分必要條件是和需要是全純函數()的實部及虛部。 因此,若在中為全純函數,就為的共軛函數。而和也是中的调和函数。 在區間內,是共軛函數的充分必要條件是和滿足柯西-黎曼方程。 (zh)
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  • p/c025040 (en)
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  • Conjugate harmonic functions (en)
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  • En matemáticas, se dice que una función de variables reales definida en un conjunto abierto conexo tiene una función conjugada si y sólo si son respectivamente las partes reales e imaginarias de un función holomorfa de variable compleja Es decir, es conjugada de si y solo si es holomorfa en . Como primera consecuencia de la definición, ambas funciones son armónicas en . Además, si existe la conjugada de esta es única salvo una constante aditiva. (es)
  • In mathematics, a real-valued function defined on a connected open set is said to have a conjugate (function) if and only if they are respectively the real and imaginary parts of a holomorphic function of the complex variable That is, is conjugate to if is holomorphic on As a first consequence of the definition, they are both harmonic real-valued functions on . Moreover, the conjugate of if it exists, is unique up to an additive constant. Also, is conjugate to if and only if is conjugate to . (en)
  • 在數學中,調和共軛(Harmonic conjugate)是針對函數的概念。定義在開集中的函數,另一個函數為其共軛函數的充分必要條件是和需要是全純函數()的實部及虛部。 因此,若在中為全純函數,就為的共軛函數。而和也是中的调和函数。 在區間內,是共軛函數的充分必要條件是和滿足柯西-黎曼方程。 (zh)
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  • Conjugado armónico (es)
  • Harmonic conjugate (en)
  • 調和共軛 (zh)
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