Let $(a,b,c)$ be a triple of complex numbers with $c$ not belonging to the set of negative integers. For a complex number $w$ and a non negative integer $n$ use Pochhammer symbol $(w)_n$ , to denote the expression : $$(w)_n=w(w+1)\dots(w+n-1).$$ The Gauss hypergeometric function, $_{2}F_{1}$ is then defined by the following power series expansion : $$_2F_1(a,b;\,c\,;z)=\sum_{n=0}^{\infty} \frac{(a)_n(b)_n}{(c)_{n}n!}z^n.$$