# (c-2a-(b-a)z)2F1+a(1-z)2F1(a+1)-(c-a)2F1(a-1)=0

The following formula holds: $$(c-2a-(b-a)z){}_2F_1(a,b;c;z)+a(1-z){}_2F_1(a+1,b;c;z)-(c-a){}_2F_1(a-1,b;c;z),$$ where ${}_2F_1$ denotes the hypergeometric 2F1.