query: If $f(z)^N$ is analytic then $f(z)$ is analytic
positive_passages.docid: 132663
positive_passages.text: Show $f$ is analytic if $f^8$ is analytic
negative_passages.docid: 19178
negative_passages.text: $f$ continuous, $f^N$ analytic on a domain D implies $f$ analytic on D
negative_passages.docid: 74622
negative_passages.text: Composition of holomorphic functions is holomorphic
negative_passages.docid: 141115
negative_passages.text: $f$ be an analytic function defined on $\mathbb{D}=\{z\in\mathbb{C}:|z|<1\}$
negative_passages.docid: 19399
negative_passages.text: $f^2$ and $f^3$ are holomorphic implies $f$ is holomorphic.
negative_passages.docid: 84103
negative_passages.text: Let $f(z)$ be entire function. Show that if $f(z)$ is real when $|z| = 1$, then $f(z)$ must be a constant function using Maximum Modulus theorem
negative_passages.docid: 89050
negative_passages.text: If $|f(z)|\leq |f(z^2)|$ on the unit disk, show that $f$ is a constant function.
negative_passages.docid: 142079
negative_passages.text: If $f$ is a non-constant analytic function on $B$ such that $|f|$ is a constant on $\partial B$, then $f$ must have a zero in $B$
negative_passages.docid: 35184
negative_passages.text: If $z_n \to z$ then $(1+z_n/n)^n \to e^z$
negative_passages.docid: 102553
negative_passages.text: How to show that $f(z) = f(i)$
negative_passages.docid: 143880
negative_passages.text: Radius of Convergence of power series of Complex Analysis
negative_passages.docid: 8039
negative_passages.text: an analytic function from unit disk to unit disk with two fixed point
negative_passages.docid: 25633
negative_passages.text: Is the function $f(z)=xy+iy$ analytic?
negative_passages.docid: 77980
negative_passages.text: How to check the real analyticity of a function?
negative_passages.docid: 55138
negative_passages.text: An analytic function $f$ on $\{z \in\mathbb{C} : |z|>1 \}$
negative_passages.docid: 20955
negative_passages.text: Let $f(z)$ be analytic on $\mathbb{D}$ = {${z\in\mathbb{C}:|z-1|<1}$} such that $f(1) = 1$, if $f(z) = f(z^2)$ for all $z\in\mathbb{D}$,
negative_passages.docid: 64748
negative_passages.text: analytic in open unit disk,corresponding to a bounded sequence and a bounded functional sequence