(c-a-1)2F1+a2F1(a+1)-(c-1)2F1(c-1)=0

Theorem

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

References

• 1953: Harry Bateman: Higher Transcendental Functions Volume I ... (previous) ... (next): $\S 2.8 (35)$