F ⁡ ( 1 , a ; a + 1 ; − 1 ) = 1 2 ⁢ a ⁢ ( ψ ⁢ ( 1 2 ⁢ a + 1 2 ) − ψ ⁡ ( 1 2 ⁢ a ) ) F\left(1,a;a+1;-1\right)={\tfrac {1}{2}}a\left(\psi \left({\tfrac {1}{2}}a+{\tfrac {1}{2}}\right)-\psi \left({\tfrac {1}{2}}a\right)\right)