lambda elliptic function | lambda modular function

The elliptic lambda function λ(τ) is a λ-modular function defined on the upper half-plane by λ(τ) congruent (ϑ_2^4(0, q))/(ϑ_3^4(0, q)), where τ is the half-period ratio, q is the nome q congruent e^(i πτ) and ϑ_i(z, q) are Jacobi theta functions. The elliptic lambda function is essentially the same as the inverse nome, the difference being that elliptic lambda function is a function of the half-period ratio τ, while the inverse nome is a function of the nome q, where q is itself a function of τ.

Dedekind eta function | elliptic alpha function | elliptic integral of the first kind | elliptic integral singular value | elliptic modulus | inverse nome | Jacobi theta functions | j-function | Klein's absolute invariant | modular function | modular group Λ | Ramanujan g- and G-functions | Weber functions