lim z → 1 − F ( a , b ; c ; z ) ( 1 − z ) c − a − b = Γ ( c ) Γ ( a + b − c ) Γ ( a ) Γ ( b ) \lim_{z\to 1-}\frac{F\left(a,b;c;z\right)}{(1-z)^{c-a-b}}=\frac{\Gamma\left(c\right)\Gamma\left(a+b-c\right)}{\Gamma\left(a\right)\Gamma\left(b\right)}