This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
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# JacobiZeta

 JacobiZetagives the Jacobi zeta function .
• Mathematical function, suitable for both symbolic and numerical manipulation.
• The Jacobi zeta function is given in terms of elliptic integrals by .
• For certain special arguments, JacobiZeta automatically evaluates to exact values.
• JacobiZeta can be evaluated to arbitrary numerical precision.
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 Scope   (9)
Evaluate for complex arguments and parameters:
Evaluate to high precision:
The precision of the output tracks the precision of the input:
Simple exact results are generated automatically:
Series expansion at the origin in the parameter:
Find series expansions at branch points and branch cuts:
Find limits at branch cuts:
Infinite arguments give symbolic results:
JacobiZeta can be applied to a power series:
 Applications   (3)
Plot of the real part of JacobiZeta over the complex plane:
Supersymmetric zero-energy solution of the Schrödinger equation in a periodic potential:
Check the Schrödinger equation:
Plot the superpotential, the potential, and the wave function:
Define a conformal map:
Use FunctionExpand to express JacobiZeta in terms of incomplete elliptic integrals:
Expand special cases:
Some special cases require argument restrictions:
Numerically find a root of a transcendental equation:
Machine-precision input is insufficient to give a correct answer:
A larger setting for \$MaxExtraPrecision can be needed:
The alternative definition requires JacobiAmplitude:
Mathematica uses the following definition:
In traditional form the vertical separator must be used:
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