- 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.
Examplesopen allclose all
Basic Examples (3)
Numerical Evaluation (4)
Specific Values (3)
Plot the EllipticTheta function for various parameters:
Generalizations & Extensions (1)
EllipticTheta can be applied to a power series:
The number of representations of n 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 point-like ions:
Plot the potential in a plane through the crystal:
A concise form of the Poisson summation formula:
Properties & Relations (2)
Numerically find a root of a transcendental equation:
Sum can generate elliptic theta functions:
Possible Issues (3)
Neat Examples (1)
Visualize a function with a boundary of analyticity: