SearchOnMath

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

Factorials apply only to nonnegative integers but can be extended to complex numbers with positive real parts using the Gamma function, \(\Gamma(n) = \int_0^\infty e^{-x}x^{n-1}dx\).

In Einstein's special relativity, the rest energy of a mass \(m\) is \(E = mc^2\), where \(c\) is the speed of light in a vacuum.