For questions related to the binomial theorem, which describes the algebraic expansion of powers of binomials.

The binomial theorem states that for $n$ a positive integer $$(x+y)^n=\sum_{k=0}^n\binom nkx^ky^{n-k}$$ with the binomial coefficient $\binom nk=\frac{n!}{k! (n - k)!}$, and the convention $0^0=1$ is observed.

This can be extended as the binomial series, an infinite series representation for functions of the form $(1 + x)^{\alpha}$, where $\alpha$ is an arbitrary complex number. See the tags gamma-function or pochhammer-symbol for information on how to generalize $\alpha !$ to arbitrary complex numbers.

Source: Binomial theorem.