This is documentation for Mathematica 3, which was
based on an earlier version of the Wolfram Language.
 EllipticNomeQ 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: In[1]:= Out[1]= This is the derivative. In[2]:= Out[2]= 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. In[3]:= There is a branch cut along the ray . Evaluate the cell to see the graph. In[4]:= This shows approximately the range of EllipticNomeQ inside the unit circle. Evaluate the cell to see the graph. In[5]:=