query: Functions $g(x)/h(x),h(x)/f(x)$ are constant
positive_passages.docid: 142494
positive_passages.text: Functions $f(x)/g(x), g(x)/h(x),h(x)/f(x)$ are constant
negative_passages.docid: 69804
negative_passages.text: Prove that if $f$ is entire and $\vert f(z^2) \vert \leq 2 \vert f(z) \vert$, then $f$ is constant
negative_passages.docid: 75479
negative_passages.text: Proving that this function is continuous on $G\times G$
negative_passages.docid: 133837
negative_passages.text: Entire function dominated by another entire function is a constant multiple
negative_passages.docid: 153855
negative_passages.text: Complex analysis, showing a function is constant
negative_passages.docid: 130537
negative_passages.text: Proving that $d(f,g)=\|f-g\| = \sup \limits_{0\leq x \leq 1} |f(x)-g(x)|$ is a metric on $X=C[0,1]$
negative_passages.docid: 158407
negative_passages.text: derivative bounded by a constant multiple of the function
negative_passages.docid: 28315
negative_passages.text: Monotone functions and non-vanishing of derivative
negative_passages.docid: 94597
negative_passages.text: $f, g$ entire functions with $f^2 + g^2 \equiv 1 \implies \exists h $ entire with $f(z) = \cos(h(z))$ and $g(z) = \sin(h(z))$
negative_passages.docid: 53024
negative_passages.text: $f(x)f(1/x)=f(x)+f(1/x)$
negative_passages.docid: 62640
negative_passages.text: Show a given analytic function is constant
negative_passages.docid: 28399
negative_passages.text: Showing $f$ is constant
negative_passages.docid: 75638
negative_passages.text: Let $u:\mathbb{C}\rightarrow\mathbb{R}$ be a harmonic function such that $0\leq f(z)$ for all $ z \in \mathbb{C}$. Prove that $u$ is constant.
negative_passages.docid: 128477
negative_passages.text: Entire function constant, where $f(z)=f(z+1)$ and $|f(z)|< e^{|z|}$.
negative_passages.docid: 59850
negative_passages.text: If $f$,$g$ and $\overline{f}g$ are holomorphic on $\Omega$, then $g=0$ or $f$ is constant
negative_passages.docid: 104044
negative_passages.text: Prove continuous functions $f$ and $g$ are equal
negative_passages.docid: 104369
negative_passages.text: If $f$ continuous and $f(x^2) = f(x)$, then $f$ is a const