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)}}