query: Suppose f(z)=u+iv is analytic. Under what circumstances will g(z)=u-iv be analytic?
positive_passages.docid: 23842
positive_passages.text: $f,\overline f$ are both analytic in a domain $\Omega$ then $f$ is constant?
negative_passages.docid: 120985
negative_passages.text: Prove that $\mathrm{Res}[f/g,z_0]=\frac{f(z_0)}{g'(z_0)}$
negative_passages.docid: 138329
negative_passages.text: Complex Analysis analytic function problem
negative_passages.docid: 154742
negative_passages.text: If $f(z)$ analytic in the domain $D$ and $f'(z)=0$ so $f(z)=$constant?
negative_passages.docid: 125566
negative_passages.text: The Identity Theorem for real analytic functions
negative_passages.docid: 111760
negative_passages.text: If $f^2$ is an analytic function then so is $f$
negative_passages.docid: 48619
negative_passages.text: Let $f$ be a non-constant analytic function on $\mathbb{D}$ satisfying $|f(z^2)| ≤ |f(z)|$ for $|z| < 1.$
negative_passages.docid: 11062
negative_passages.text: $f(z)=\frac1{2\pi i}\int_{\Gamma}\frac{f(\zeta)}{z-\zeta}d\zeta$ if $\lim_{z\to\infty}f(z)=0$ and $f$ is analytic in $|z|\ge1$
negative_passages.docid: 43440
negative_passages.text: Complex Analysis: Showing analytic function is zero
negative_passages.docid: 64172
negative_passages.text: Show that if $f$ is analytic in a domain $D$ and $|f(z)|$ is constant in $D$, then the function $f(z)$ is constant in $D$
negative_passages.docid: 93400
negative_passages.text: Prove that an analytic function with a constant imaginary part is constant itself
negative_passages.docid: 3349
negative_passages.text: For $f$ an analytic function, what is
negative_passages.docid: 18611
negative_passages.text: An analytic function with a simple pole
negative_passages.docid: 96427
negative_passages.text: Why $f^{\prime}(z)=u_{x}+iv_{x}$?
negative_passages.docid: 50115
negative_passages.text: Show that the holomorphic function $u + iv$ must be constant if $u = h \circ v$. Problem from Remmert.
negative_passages.docid: 118136
negative_passages.text: Finding univalent function with $f(z_1)=z_2$
negative_passages.docid: 62640
negative_passages.text: Show a given analytic function is constant