# Tagged Questions

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### What functions satisfy this functional equation?

$$f(x)-g(x)=f(g(x))$$ How could I find an f(x) and g(x) that satisfy this?
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### Functional equation $(1-z)f(x)=f(\frac{1-z}{z}f(xz))$

May you could help me with the following functional equation: $(1-z)f(x)=f(\frac{1-z}{z}f(xz))$. I want to find all function $f:[0,\infty)\rightarrow[0,\infty)$ for $x>0,0<z<1$ Its an ...
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### Is there a function $f$ such that $\Gamma (c+x)=\Gamma (c-f\left( x \right) )$?

I was just looking at Euler's reflection formula for Gamma function which states $$\Gamma (1-z)\Gamma (z)=\frac { \pi }{ \sin { (z\pi ) } }$$ but it seems to me that one more reflection formula ...
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### More general reflection formula for Gamma function

It is know that $\Gamma(z)\, \Gamma{(1-z)}=\pi \csc( \pi z)$. Is there any formula for $\Gamma{(a+z)}\Gamma{(a-z)}$ where $a$ is a rational number, i. e., $a=p/k$ with $p, k$ integers and $z$ is ...
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### Inverse function of $y=W(e^{ax+b})-W(e^{cx+d})+zx$

I have a simple question for which I am looking for a closed form expression (If there exits one). In other words, given: $$y=W(e^{ax+b})-W(e^{cx+d})+zx$$ where $W$ is the Lambert $W$ function and ...
For instance, there is functional equation for Lambert W function $z=W(z) e^{W(z)}$ And moreover, there is differential one: $z(1+W)\frac{dW}{dz}=W$. At the same time, there is no known functional ...