Define the nome by q = e^(-π K'(k)/K(k)) = e^(i πτ), where K(k) is the complete elliptic integral of the first kind with modulus k, K'(k) = K(sqrt(1 - k^2)) is the complementary complete elliptic integral of the first kind, and τ is the half-period ratio.

Dedekind eta function | q-Pochhammer symbol | q-series identities