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  • EllipticNomeQ[ m ] gives the nome q corresponding to the parameter m in an elliptic function.
  • Mathematical function (see Section A.3.10).
  • EllipticNomeQ is related to EllipticK by .
  • EllipticNomeQ[ m ] has a branch cut discontinuity in the complex m plane running from to .
  • See the Mathematica book: Section 3.2.11.
  • See also: InverseEllipticNomeQ.

    Further Examples

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



    This is the derivative.



    As approaches 1 from below along the real line, approaches 1 very abruptly. In order to obtain meaningful values for the function in the neighborhood of 1, it is a good idea to use multiple precision.

    Evaluate the cell to see the graph.


    There is a branch cut along the ray .

    Evaluate the cell to see the graph.


    This shows approximately the range of EllipticNomeQ inside the unit circle.

    Evaluate the cell to see the graph.