SearchOnMath

Prime numbers are key to Euler's product formula, \(\sum_{k=1}^{\infty}\frac{1}{k^s}=\prod_{p \;\; \mathrm{prime}}\frac{1}{1-p^{-s}}\), which establishes equality between an infinite sum and product for fixed \(s>1\).

The heat equation, \(\frac{\partial \varnothing}{\partial t} = D \nabla^2 \varnothing\), uses the Laplacian of \(\varnothing\) to express diffusion through a medium.

Shannon's entropy, \(H(X) = -\sum_{x \in \mathbf{X}} p(x) \log p(x)\), measures how informative the mass function \(p\) is about the occurrence of the possible values of variable \(X\).