Understanding the generalised binomial theorem

59 Views Asked by At

In lecture we wrote the following:

Generalised Binomial Theorem: For any $\alpha \in \mathbb{C}$ holds

$$(1+x)^\alpha = \sum_{k=0}^\infty \binom{\alpha}{k} x^k$$

where $x$ is a formal variable or $x \in \mathbb{C}$ with $\lvert x \rvert \le 1$.

But what is a formal variable? Does that mean that I can, for example, plug in a formal power series $A(z)$ for $x$?