# Tagged Questions

**9**

votes

**2**answers

423 views

### Series defined by a fixed-point functional equation

Description
I my work, I met fixed-point functional equations of a very specific form. Since I am not expert in the domain of functional equations, I have not pushed the study of these very far. Here ...

**35**

votes

**10**answers

5k views

### The functional equation $f(f(x))=x+f(x)^2$

I'd like to gather information and references on the following functional equation for power series $$f(f(x))=x+f(x)^2,$$$$f(x)=\sum_{k=1}^\infty c_k x^k$$
(so $c_0=0$ is imposed).
First things that ...

**1**

vote

**1**answer

638 views

### Infinite graphs as functional operators

Original Question
Consider an infinite tree of constant degree $k$. For such a tree we can consider the total number of nodes at depth $n$, $g(f)$, and the total number of paths from the root, ...

**2**

votes

**0**answers

217 views

### Algebraic Dirichlet series and beyond

I wonder what the "right" notion of "algebraic Dirichlet series" might be. Here I'm thinking of formal Dirichlet series $D(s)=\sum_{n\geq 1} a_n/n^s$, say with $a_n$ being rational numbers.
I'm ...

**5**

votes

**1**answer

703 views

### beyond differentially algebraic power series

In a recent question, we learned about the existence of functions that do not satisfy any algebraic differential equation.
One nice property of such equations is that there is a good way to ...