Expansions on branch cuts

Formulas on real axis for real m

For m>1,csc^-1(m^1/2)+Pi u<xu+1/2)/;u ∈ Z

For m>1,Pi(u+1/2)<xu+1)-csc^-1(m^1/2)/;u ∈ Z

Formulas for vertical intervals

For Re(z₀/2 Pi-1/4) ∈ Z

For Re(z₀/2 Pi-3/4) ∈ Z