Gauss summation theorem and its applications (Q2757184)

The authors present a survey of the various well-known derivations of the Gauss summation theorem: NEWLINE\[NEWLINE_2F_1(a,b;c;1)= {\Gamma(c) \Gamma (c-a-b) \over \Gamma(c-a) \Gamma(c-b)}NEWLINE\]NEWLINE NEWLINE\[NEWLINE(\text{Re} (c-a-b)>0;\;c\neq 0,-1,-2, \dots).NEWLINE\]NEWLINE A few applications of this classical result, especially in evaluating certain very simple Eulerian integrals of the first and second kind, are also considered.