All Questions

Let $A$ be a function from $[0,1]$ to $[0,1]$. $A$ is an involution if $A(A(x))=x$ for all $x\in[0,1]$. Which involutions $A$ exist such that $A(x)=\sum_{k=0}^\infty a_k x^k$ with $a_0=1$ and $a_k\...

Let $\mathcal{G}$ be the set of probability generating functions of random variables taking positive integer values, considered as functions on $[0,1]$. So $G\in\mathcal{G}$ can be written $G(x)=\...