nc⁡(z,k)-π2⁢K⁢k′⁢sec⁡ζ=-2⁢πK⁢k′⁢∑n=0∞(-1)n⁢q2⁢n+1⁢cos⁡((2⁢n+1)⁢ζ)1+q2⁢n+1,