(c-a-b)2F1+a(1-z)2F1(a+1)-(c-b)2F1(b-1)=0
From specialfunctionswiki
Theorem
The following formula holds: $$(c-a-b){}_2F_1(a,b;c;z)+a(1-z){}_2F_1(a+1,b;c;z)-(c-b){}_2F_1(a,b-1;c;z)=0,$$ where ${}_2F_1$ denotes hypergeometric 2F1.
Proof
References
- 1953: Arthur Erdélyi, Wilhelm Magnus, Fritz Oberhettinger and Francesco G. Tricomi: Higher Transcendental Functions Volume I ... (previous) ... (next): $\S 2.8 (33)$
