SearchOnMath

Another common definition of the exponential function to the natural basis, \(e^x\), comes from writing it as the series \(e^x = \sum_{k=0}^{\infty} \frac{x^k}{k!}\).

The binomial theorem, making use of the well-known binomial coefficients, allows expressing \((x+y)^n\) as a sum: \((x+y)^n=\sum_{k=0}^{n} \binom{n}{k} x^k y^{n-k}\).

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 (\(\mathcal{T}\)).