- Mathematical function, suitable for both symbolic and numerical manipulation.
- The are only defined within the unit q disk, ; the unit disk forms a natural boundary of analyticity.
- Within 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.
- EllipticTheta can be used with Interval and CenteredInterval objects. »
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Basic Examples (3)
Numerical Evaluation (5)
Specific Values (3)
Plot the EllipticTheta function for various parameters:
Function Properties (10)
Real and complex domains of EllipticTheta:
EllipticTheta is a periodic function with respect to :
EllipticTheta threads elementwise over lists:
Generalizations & Extensions (1)
EllipticTheta can be applied to a power series:
The number of representations of as a sum of four squares:
Conformal map from an ellipse to the unit disk:
Visualize the map:
Green's function for the 1D heat equation with Dirichlet boundary conditions and initial condition :
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:
Form any elliptic function with given periods, poles and zeros as a rational function of EllipticTheta:
Properties & Relations (2)
Numerically find a root of a transcendental equation:
Sum can generate elliptic theta functions:
Possible Issues (4)
Neat Examples (1)
Visualize a function with a boundary of analyticity:
Wolfram Research (1988), EllipticTheta, Wolfram Language function, https://reference.wolfram.com/language/ref/EllipticTheta.html (updated 2022).
Wolfram Language. 1988. "EllipticTheta." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2022. https://reference.wolfram.com/language/ref/EllipticTheta.html.
Wolfram Language. (1988). EllipticTheta. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/EllipticTheta.html