View source for (c-2a-(b-a)z)2F1+a(1-z)2F1(a+1)-(c-a)2F1(a-1)=0

==Theorem==
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]].

==Proof==

==References==
* {{BookReference|Higher Transcendental Functions Volume I|1953|Arthur Erdélyi|author2=Wilhelm Magnus|author3=Fritz Oberhettinger|author4=Francesco G. Tricomi|prev=findme|next=(b-a)2F1+a2F1(a+1)-b2F1(b+1)=0}}: $\S 2.8 (31)$

[[Category:Theorem]]
[[Category:Unproven]]