In what follows, we introduce the classical Gamma function in Sect. 2.1. It is essentially understood to be a generalized factorial. However, there are many further applications, e.g., as part of probability distributions (see, e.g., Evans et al. 2000). The main properties of the Gamma function are explained in this chapter (for a more detailed discussion the reader is referred to, e.g., Artin (1964), Lebedev (1973), Muller (1998), Nielsen (1906), and Whittaker and Watson (1948) and the references therein).