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EllipticTheta
EllipticTheta[
a
,
u
,
q
] gives the theta function  ( ).
Mathematical function (see Section A.3.10).
 ,  ,  ,  .
See Section 3.2.11 for a discussion of argument conventions for elliptic and related functions.
See the Mathematica book: Section 3.2.11.
See also: ModularLambda, DedekindEta, KleinInvariantJ.
Further Examples
The third argument of EllipticTheta should be a complex number with absolute value less than 1. This argument is the nome corresponding to the modulus employed by most other elliptic functions. See EllipticNomeQ.
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The Jacobi elliptic functions (sn and friends) are often expressed in terms of theta functions, which can be computed very efficiently.
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This is the derivative.
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