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

# EllipticTheta

 EllipticThetagives the theta function .
• 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.
Series expansion:
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Series expansion:
 Out[1]=
 Scope   (6)
Evaluate numerically for complex arguments:
Evaluate to high precision:
The precision of the output tracks the precision of the input:
EllipticTheta evaluates symbolically for special arguments:
EllipticTheta can be applied to a power series:
 Applications   (7)
Plot near the unit circle in the complex q plane:
The number of representations of as a sum of four squares:
Conformal map from an ellipse to the unit disk:
Visualize the map:
Dirichlet Green's function for the 1D heat equation:
Plot the time-dependent temperature distribution:
Form Bloch functions of a one-dimensional crystal with Gaussian orbitals:
Plot Bloch functions as a function of the quasi-wave vector:
Electrostatic potential in a NaCl-like crystal with pointlike ions:
Plot the potential in a plane through the crystal:
A concise form of the Poisson summation formula:
Numerically find a root of a transcendental equation:
Sum can generate elliptic theta functions:
Machine-precision input is insufficient to give a correct answer:
Use arbitrary-precision arithmetic to obtain the correct result:
EllipticTheta has the attribute NHoldFirst:
Different argument conventions exist:
Visualize a function with a boundary of analyticity:
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