DedekindEta

DedekindEta[τ]

gives the Dedekind eta modular elliptic function .

Details

  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • DedekindEta is defined only in the upper half of the complex τ plane. It is not defined for real τ.
  • The argument τ is the ratio of Weierstrass halfperiods .
  • DedekindEta satisfies where is the discriminant, given in terms of Weierstrass invariants by .
  • For certain special arguments, DedekindEta automatically evaluates to exact values.
  • DedekindEta can be evaluated to arbitrary numerical precision.
  • DedekindEta automatically threads over lists.

Examples

open allclose all

Basic Examples  (2)

Evaluate numerically:

In[1]:=
Click for copyable input
Out[1]=
In[1]:=
Click for copyable input
Out[1]=

Scope  (4)

Applications  (2)

Properties & Relations  (2)

See Also

ModularLambda  KleinInvariantJ  EllipticTheta  PartitionsP  QPochhammer

Tutorials

Introduced in 1996
(3.0)