WeierstrassSigma
WeierstrassSigma[u,{g2,g3}]
gives the Weierstrass sigma function .
Details

- Mathematical function, suitable for both symbolic and numerical manipulation.
- Related to WeierstrassZeta by the differential equation
.
- WeierstrassSigma is not periodic and is therefore not strictly an elliptic function.
- For certain special arguments, WeierstrassSigma automatically evaluates to exact values.
- WeierstrassSigma can be evaluated to arbitrary numerical precision.
Examples
open allclose allBasic Examples (4)
Scope (25)
Numerical Evaluation (4)
Specific Values (3)
WeierstrassSigma automatically evaluates to simpler functions for certain parameters:
Find the first positive maximum of WeierstrassSigma[x,1/2,1/2]:
Visualization (2)
Plot the WeierstrassSigma function for various parameters:
Function Properties (11)
WeierstrassSigma is defined for all real and complex inputs:
Approximate function range of :
WeierstrassSigma is an odd function with respect to x:
WeierstrassSigma threads elementwise over lists in its first argument:
It has no singularities or discontinuities:
is neither nondecreasing nor nonincreasing:
is neither non-negative nor non-positive:
is neither convex nor concave:
TraditionalForm formatting:
Differentiation (2)
Series Expansions (3)
Find the Taylor expansion using Series:
Plots of the first three approximations around :
Applications (2)
The system of coupled nonlinear differential equations for a heavy symmetric top:
The solutions can be expressed through Weierstrass sigma and zeta functions:
Numerically check the correctness of the solutions:
Form any elliptic function with given periods, poles and zeros as a rational function of WeierstrassSigma:
Form an elliptic function with a single and a double zero and a triple pole:
Neat Examples (1)
Plot WeierstrassSigma over the complex plane:
Text
Wolfram Research (1996), WeierstrassSigma, Wolfram Language function, https://reference.wolfram.com/language/ref/WeierstrassSigma.html.
CMS
Wolfram Language. 1996. "WeierstrassSigma." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/WeierstrassSigma.html.
APA
Wolfram Language. (1996). WeierstrassSigma. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/WeierstrassSigma.html