This is documentation for Mathematica 3, which was
based on an earlier version of the Wolfram Language.
 DedekindEta DedekindEta[] gives the Dedekind eta modular elliptic function . Mathematical function (see Section A.3.10). DedekindEta is defined only in the upper half of the complex plane. It is not defined for real . The argument is the ratio of Weierstrass half-periods . DedekindEta satisfies where is the discriminant, given in terms of Weierstrass invariants by . See SectionÂ 3.2.11 for a discussion of argument conventions for elliptic functions. See the Mathematica book: Section 3.2.11. See also: ModularLambda, KleinInvariantJ, EllipticTheta, PartitionsP. Further Examples The Dedekind eta function is defined by , for in the complex upper half-plane. If is regarded as the ratio of half-periods of an elliptic curve and are the corresponding Weierstrass coefficients, then . In[1]:= Out[1]= Under fractional linear transformations of the complex plane with integer coefficients, the Dedekind eta function transforms in simple ways. The most obvious example of such a transformation (apart from the identity) is ; in this case . In[2]:= Out[2]= In[3]:= Out[3]= In[4]:=