query: Analytic properties of a function such that $f(x)-f(y)=f(x/y)$.
positive_passages.docid: 151573
positive_passages.text: Show f is continuous on (0, ∞) iff f is continuous at 1 for a defined function.
negative_passages.docid: 19178
negative_passages.text: $f$ continuous, $f^N$ analytic on a domain D implies $f$ analytic on D
negative_passages.docid: 21891
negative_passages.text: If $f(xy)=f(x)f(y)$ then show that $f(x) = x^t$ for some t
negative_passages.docid: 131357
negative_passages.text: Prove that $f(x,y)=xy$ is differentiable using the definition
negative_passages.docid: 43177
negative_passages.text: How do I rigorously show $f(z)$ is analytic if and only if $\overline{f(\bar{z})}$ is?
negative_passages.docid: 109942
negative_passages.text: Find continuous functions such that $f(x+y)+f(x-y)=2[f(x)+f(y)]$
negative_passages.docid: 28620
negative_passages.text: Function $f(z)$ such that $|f(z)| > |z|$ for every $z\in\mathbb{C}, 1/f(z)$
negative_passages.docid: 103251
negative_passages.text: Solution(s) to $f(x + y) = f(x) + f(y)$ (and miscellaneous questions...)
negative_passages.docid: 80210
negative_passages.text: It is posible to have a function $f$ with the following property?
negative_passages.docid: 91430
negative_passages.text: If $f$ is twice differentiable, $\big(f(y) - f(x)\big)/(y-x)$ is differentiable
negative_passages.docid: 24306
negative_passages.text: Is there a continuous function $f(x)$ such that the inverse function is $1/f(x)$?
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: 30204
negative_passages.text: Prove that $f'(0)$ exists and $f'(0) = b/(a - 1)$
negative_passages.docid: 111470
negative_passages.text: Proof of differentiability of $f(x)$
negative_passages.docid: 3349
negative_passages.text: For $f$ an analytic function, what is
negative_passages.docid: 148247
negative_passages.text: Prove the existence of an analytic function
negative_passages.docid: 9844
negative_passages.text: Proof composition of analytic functions is analytic