F ( x , s ) = Γ ( 1 − s ) ( 2 π ) 1 − s ( e π i ( 1 − s ) / 2 ζ ( 1 − s , x ) + e π i ( s − 1 ) / 2 ζ ( 1 − s , 1 − x ) ) F\left(x,s\right)=\frac{\Gamma\left(1-s\right)}{(2\pi)^{1-s}} \left(e^{\pi i(1-s)/2}\zeta\left(1-s,x\right)+e^{\pi i(s-1)/2}\zeta\left(1-s,1-x\right)\right)