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Analytic and Harmonic Functions
29
Flashcards
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f(z) = z*
Neither analytic nor harmonic
f(z) = \sqrt{z}
Analytic
f(z) = \tan^{-1}(z)
Analytic
f(z) = \cosh(z)
Analytic
f(z) = \frac{\overline{z}}{z}
Neither harmonic nor analytic
f(z) = e^z
Analytic
f(z) = \ln(z)
Analytic
f(z) = \sinh(z)
Analytic
f(z) = \tan(z)
Analytic
f(z) = e^{\overline{z}}
Neither harmonic nor analytic
f(z) = \frac{1}{\overline{z}}
Neither harmonic nor analytic
f(z) = z^n, n\in\mathbb{Z}, n > 0
Analytic
f(z) = e^{i|z|}
Neither harmonic nor analytic
f(z) = \sin(z)
Analytic
f(z) = \mathrm{Arg}(z)
Neither harmonic nor analytic
f(z) = \mathrm{Re}(z)
Harmonic but not analytic
f(z) = e^{|z|}
Neither harmonic nor analytic
f(z) = z^* + z
Harmonic but not analytic
f(z) = \cos(z)
Analytic
f(z) = \frac{d}{dz}z^n, n\in\mathbb{Z}, n > 0
Analytic
f(z) = \frac{\sin(z)}{z}, z\neq 0
Analytic
f(z) = z \overline{z}
Harmonic but not analytic
f(z) = \mathrm{Im}(z)
Harmonic but not analytic
f(z) = \log|z|
Harmonic but not analytic
f(z) = \overline{z}^2
Neither harmonic nor analytic
f(z) = z \cdot \overline{z} + i
Neither harmonic nor analytic
f(z) = |z|^2
Harmonic but not analytic
f(z) = \frac{1}{z}
Analytic
f(z) = \frac{\mathrm{Re}(z)}{z}
Neither harmonic nor analytic
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