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)