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

- Mathematical function, suitable for both symbolic and numerical manipulation.
- InverseEllipticNomeQ[q] yields the unique value of the parameter m which makes EllipticNomeQ[m] equal to q.
- The nome q must always satisfy
.
- InverseEllipticNomeQ can be evaluated to arbitrary numerical precision.
- InverseEllipticNomeQ automatically threads over lists.
Examples
open allclose allBasic Examples (4)
Scope (24)
Numerical Evaluation (4)
Specific Values (4)
Find a value of for which InverseEllipticNomeQ[x]=0.9:
Visualization (2)
Plot the InverseEllipticNomeQ function for various parameters:
Function Properties (10)
Real domain of InverseEllipticNomeQ:
Complex domain of InverseEllipticNomeQ:
InverseEllipticNomeQ threads element-wise over lists:
InverseEllipticNomeQ is an analytic function over its real domain:
In general, it has both singularities and discontinuities:
InverseEllipticNomeQ is nondecreasing over its real domain:
InverseEllipticNomeQ is injective:
InverseEllipticNomeQ is not surjective:
InverseEllipticNomeQ is neither non-negative nor non-positive:
InverseEllipticNomeQ is concave over its real domain:
TraditionalForm formatting:
Differentiation (2)
Series Expansions (2)
Find the Taylor expansion using Series:
Generalizations & Extensions (1)
InverseEllipticNomeQ can be applied to power series:
Applications (4)
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:
Find the modulus corresponding to the elliptic curve, specified by Weierstrass invariants:
Compute the modulus alternatively using InverseEllipticNomeQ:
Properties & Relations (5)
Possible Issues (2)
InverseEllipticNomeQ remains unevaluated outside its domain of analyticity:
InverseEllipticNomeQ is single valued, and EllipticNomeQ is multivalued:
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