The inverse nome function is essentially the same as the elliptic lambda function, the difference being that elliptic lambda function is a function
of the half-period ratio , while the inverse nome is a function of the nome , where is itself a function of .

As a rule, inverse and direct functions satisfy the relation -for example, . The inverse nome is an exception to this
rule due to a historical mistake made more a century ago. In particular, the inverse
nome and nome itself are connected by the opposite relation
.

Special values include

(3)

(4)

(5)

although strictly speaking, is not defined at 1 because is a modular function, therefore has a dense set of
singularities on the unit circle, and is therefore only defined strictly inside the
unit circle.