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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]:= 
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