EllipticTheta

EllipticTheta[a,u,q]

gives the theta function .

EllipticTheta[a,q]

gives the theta constant .

Details

  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • The are defined only inside the unit q disk; the disk forms a natural boundary of analyticity.
  • Inside the unit q disk, and have branch cuts from to .
  • For certain special arguments, EllipticTheta automatically evaluates to exact values.
  • EllipticTheta can be evaluated to arbitrary numerical precision.
  • EllipticTheta automatically threads over lists.

Examples

open allclose all

Basic Examples  (2)

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

Series expansion:

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

Scope  (6)

Generalizations & Extensions  (1)

Applications  (7)

Properties & Relations  (2)

Possible Issues  (3)

Neat Examples  (1)

See Also

ModularLambda  DedekindEta  KleinInvariantJ  SiegelTheta  QPochhammer  EllipticThetaPrime

Tutorials

Introduced in 1988
(1.0)
| Updated in 2017
(11.2)