View source for C(a-(c-b)z)2F1-ac(1-z)2F1(a+1)+(c-a)(c-b)z2F1(c+1)=0

==Theorem==
The following formula holds:
$$c(a-(c-b)z){}_2F_1(a,b;c;z)-ac(1-z){}_2F_1(a+1,b;c;z)+(c-a)(c-b)z{}_2F_1(a,b;c+1;z)=0,$$
where ${}_2F_1$ denotes [[hypergeometric 2F1]].

==Proof==

==References==
* {{BookReference|Higher Transcendental Functions Volume I|1953|Arthur Erdélyi|author2=Wilhelm Magnus|author3=Fritz Oberhettinger|author4=Francesco G. Tricomi|prev=(c-a-b)2F1+a(1-z)2F1(a+1)-(c-b)2F1(b-1)=0|next=(c-a-1)2F1+a2F1(a+1)-(c-1)2F1(c-1)=0}}: $\S 2.8 (34)$

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