Gauss Hypergeometric Function

Gauss hypergeometric function \({ }_{2}F_{1} \) is the most important of all hypergeometric functions and the one which has been the most largely studied. In Sects. 4.1 and 4.2, we present its first properties, which are special cases of the general properties of hypergeometric functions. In Sect. 4.3, we give the 24 Kummer’s solutions of the Gauss hypergeometric equation. This enables us to prove in Sects. 4.4, 4.5, and 4.6 some transformation and summation formulas.