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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:
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Series expansion:
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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:
TraditionalForm formatting:
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:
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