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Mathematics
The limit definition of the exponential function
A definition of the exponential function that has found application in numerous approximation schemes is \(e^x = \lim_{y\to\infty} \left(1+\frac{x}{y}\right)^y\).
Mathematics
The integral definition of the exponential function
The exponential function to the natural base, \(e^x\), can be defined in more than one way. One of them makes use of the integral \(\int_1^{e^x} \frac{dy}{y}= x\).
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 (\(\mathcal{T}\)).