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InverseEllipticNomeQ

  • InverseEllipticNomeQ[ q ] gives the parameter m corresponding to the nome q in an elliptic function.
  • Mathematical function (see Section A.3.10).
  • InverseEllipticNomeQ[ q ] yields the unique value of the parameter which makes EllipticNomeQ[ m ] equal to .
  • The nome must always satisfy .
  • See the Mathematica book: Section 3.2.11.
  • See also: EllipticNomeQ.

    Further Examples

    Certain elliptic functions, such as the theta functions, traditionally use the nome as their argument; others use the modulus . InverseEllipticNomeQ returns the modulus corresponding to a given nome. This function is inverse to EllipticNomeQ.

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    The range of EllipticNomeQ is illustrated in the Further Examples for that function. InverseEllipticNomeQ can be extended outside this range. Thus extended, it is no longer a one-to-one function, and so not strictly an inverse to EllipticNomeQ.

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    It is a good idea to use multiple precision when the argument is a real number greater than 1/2.

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