Q-function (RL)

Suppose we are in a Markov decision process and using discounted rewards define the Q-function $Q : S \times A \rightarrow \mathbb{R}$ as the solution to the following equations

$$Q(s,a) = R(s, a) + \gamma \sum_{s' \in S} T(s,a,s') \max_{a' \in A_{s'}} Q(s', a').$$