Consider the following differential equation $$F(cx) = F(x) + x F'(x)$$ for $c>1$. Does this differential equation belong to a some well known class? Is there a way to find all the solutions ...
I have arrived to this equation in several contexts within branching processes. It arises from textbook exercises, so it must be solvable somehow. Here $f$ is a probability generating function which ...
Maxwell's theorem (after James Clerk Maxwell) says that if a function $f(x_1,\ldots,x_n)$ of $n$ real variables is a product $f_1(x_1)\cdots f_n(x_n)$ and is rotation-invariant in the sense that the ...
Edited: I want to get a sentiment score of various sentences and I've tried coming up with an equation that could satisfy the conditions that are inherent to each sentence (It's estimated mood as ...