A powerful search engine for mathematical formulas with LaTeX support
Check out the examples below▽
Mathematics
The closed-form expression for the Fibonacci number
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.
Physics
Einstein's field equations in general relativity
In Einstein's general relativity, the field equation \(\mathcal{G} = - \frac{8\pi G}{c^4} \mathcal{T}\) relates spacetime curvature (\(\mathcal{G}\)) to its mass-energy content (\(\mathcal{T}\)).
Mathematics
The series expansion of the natural logarithm
The natural logarithm can be expanded into a series, yielding \(\ln(1+x) = \sum_{k=1}^{\infty} \frac{(-1)^{k+1}x^k}{k}\).