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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 total probability formula, \(P(A) = \sum_k P(A \cap B_k)\), relates the occurrence of an event \(A\) to that of several mutually exclusive events (\(B_k\)'s).

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