SearchOnMath

The \(k\)th Fibonacci number can be written in closed form as \(F(k) = \frac{\varphi^k - (-\frac{1}{\varphi})^k}{\sqrt{5}}\), where \(\varphi\) is the celebrated golden ratio.

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 \(X\).

Maxwell's equations in a vacuum describe a wave propagating at speed \(c\) as the interaction of electric field \(E\) and magnetic field \(B\): \(\nabla \cdot E = 0\), \(\nabla \times E = -\frac{\partial B}{\partial t}\), \(\nabla \cdot B = 0\), \(\nabla \times B = \frac{1}{c^2} \frac{\partial E}{\partial t}\).