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# InverseEllipticNomeQ

 InverseEllipticNomeQ[q]gives the parameter m corresponding to the nome q in an elliptic function.
• Mathematical function, suitable for both symbolic and numerical manipulation.
• The nome q must always satisfy .
Evaluate numerically:
Series expansion:
Evaluate numerically:
 Out[1]=

 Out[1]=

Series expansion:
 Out[1]=
 Scope   (5)
Evaluate for complex arguments:
Evaluate to high precision:
The precision of the output tracks the precision of the input:
InverseEllipticNomeQ can be applied to power series:
 Applications   (3)
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:
New in 3