Half-period ratio
In mathematics, the half-period ratio τ of an elliptic function is the ratio τ = ω 2 ω 1 {\displaystyle \tau ={\frac {\omega _{2}}{\omega _{1}}}} of the two half-periods ω 1 2 {\displaystyle {\frac {\omega _{1}}{2}}} and ω 2 2 {\displaystyle {\frac {\omega _{2}}{2}}} of the elliptic function, where the elliptic function is defined in such a way that ℑ ( τ ) > 0 {\displaystyle \Im (\tau )>0} is in the upper half-plane. Quite often in the literature, ω1 and ω2 are defined to be the periods of an elliptic function rather than its half-periods.