In information theory, the Rényi entropy generalizes the Hartley entropy, the Shannon entropy, the collision entropy and the min-entropy. Entropies quantify the diversity, uncertainty, or randomness of a system. The entropy is named after Alfréd Rényi, who looked for the most general definition of information measures that preserve additivity for independent events. In the context of fractal dimension estimation, the Rényi entropy forms the basis of the concept of generalized dimensions.
The Rényi entropy is important in ecology and statistics as index of diversity. The Rényi entropy is also...
very simply put.
$$(fg)^{(n)} = \sum_{k=0}^n {n\choose k}f^{(n-k)}g^{(k)},$$
where ${n\choose k} = \dfrac{n!}{k!(n-k)!}$ is the binomial coefficient and $f^{(j)}$ denotes the $j$th derivative of $f$ (and in particular $f^{(0)}=f$).
Solve for n (integers only of course, not going to to play myself...
