# Tagged Questions

50 views

### A scaling functional equation

I want to find a closed form of a function satisfying $$G(4z)=\frac{G(z)}{2z},$$ unfortunately I am not experienced with scaling problems, so I have no idea and would be thankful for any hints. ...
239 views

### How to identify this power series as $k\sin(k/x)$?

In this question, a functional equation is solved for functions with a power series. We find a recursive formula: (copied from the answer by user achille hui) \begin{align} ( 2^1 - 3 ) a_2 &= 0\\ ...
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### Question about ratios and combinatorics

In this question that I posted yesterday (11/15): I am solving a programming puzzle that consists of finding all the possible ways to build a brick wall of $48$" $\times$ $10$" (width $\times$ height ...
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### Equation about generating functions and subfactorial

Suppose $G_n(w)$ is a formal power series (really a probability generating function, see the following explanation) of variable $w$, try to solve out $G_n(w)$ for all $n\ge0$ from the ...
### How to solve a functional equation of the form $1-g(f(s))=m(1-g(s))$?
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 ...
I need to find the function c(k), knowing that $$\sum_{k=0}^{\infty} \frac{c(k)}{k!}=1$$ $$\sum_{k=0}^{\infty} \frac{c(2k)}{(2k)!}=0$$ $$\sum_{k=0}^{\infty} \frac{c(2k+1)}{(2k+1)!}=1$$ ...