I know the equation $ f^{\prime} (x) = f(x) f^{\prime} (x-1) $ is solved by $f(x) = C$ or by tetration ( $ f(x+1) = \exp(f(x)) $).
So I wonder What are the solutions to
$$f ^{\prime \prime}(x) = f(x) f^{\prime \prime} (x-1) ?$$
1
I need to prove that the age behavior of the Gamma Distribution with probability density function $$ f(x)=\frac{\lambda^{\alpha}x^{\alpha-1}e^{-\lambda x}}{\Gamma(\alpha)}$$
For $x\geq 0$, $\lambda, \alpha >0$; I.e., the conditional pprobability $P(X>x+t|X>t)$, increases in $t$ whenever $\alpha >...
I know that if $f$ is surjective then $f(\mathfrak{a})$ is an ideal for every ideal $\mathfrak{a}$ in $A$. I want to first prove that if $\mathfrak{m}$ is maximal in $A$ then $f(\mathfrak{m}) = \mathfrak{m'}$ is maximal in $B$.
$A/\mathfrak{m}$ is a field by maximality of $\mathfrak{m}$ and $f$...
