θ1⁡(z|τ)=θ1′⁡(0|τ)⁢sin⁡z⁢∏n=1∞sin⁡(n⁢π⁢τ+z)⁢sin⁡(n⁢π⁢τ-z)sin2⁡(n⁢π⁢τ),