Built-in Mathematica Symbol

InverseEllipticNomeQ

InverseEllipticNomeQ[q]
gives the parameter m corresponding to the nome q in an elliptic function.

InverseEllipticNomeQ[q] yields the unique value of the parameter m which makes EllipticNomeQ[m] equal to q.

Evaluate numerically:

Series expansion:

Evaluate numerically:

Series expansion:

Evaluate for complex arguments:

Evaluate to high precision:

The precision of the output tracks the precision of the input:

InverseEllipticNomeQ threads element-wise over lists:

InverseEllipticNomeQ can be applied to power series:

Convert between elliptic modulus and nome in elliptic function identities:

Partition function for a one-atom monatomic gas in a finite container of unit length:

Form partition functions for n bosonic particles:

Calculate and plot mean energies:

InverseEllipticNomeQ is a modular function. Make an ansatz for a modular equation:

Form an overdetermined system of equations and solve it:

This is the modular equation of order 2:

Verify using Series:

Compose with inverse functions:

Find derivatives:

Symbolically solve a transcendental equation:

Numerically find a root of a transcendental equation:

Relation to q-series:

InverseEllipticNomeQ remains unevaluated outside its domain of analyticity:

InverseEllipticNomeQ is single valued, and EllipticNomeQ is multivalued: