I research in generating functions of Hyper-geometric functions $_2F_1(a+n,b;c+n;x)$ using Lie group theoretic method and so the recurrence relation is important in this method.
I want recurrence relation like these in the image
the author write that Slater in "Generalized Hypergeometric Functions" give this relations for $_2F_1(a,b;c+n;x)$
But , I don't know how to find this recurrence relation for another $_2F_1(a+n,b;c+n;x)$
Update:- Are these recurrence relation correct ? $$[z \frac{\partial}{\partial z}+c+n-1] _2F_1 (a+n,b;c+n;z)=(c+n-1) _2F_1 (a+n,b;c+n-1;z) $$
and
$$[(c+n)(1-z) \frac{\partial}{\partial z}-(c+n)(a+b-c)] _2F_1 (a+n,b;c+n;z)=(c-a)(c+n-b)_2F_1 (a+n,b;c+n+1;z) $$
please, help me in this .