WeierstrassP
WeierstrassP[u,{g2,g3}]
gives the Weierstrass elliptic function .
Details

- Mathematical function, suitable for both symbolic and numerical manipulation.
gives the value of
for which
.
- For certain special arguments, WeierstrassP automatically evaluates to exact values.
- WeierstrassP can be evaluated to arbitrary numerical precision.
Examples
open allclose allBasic Examples (4)
Scope (26)
Numerical Evaluation (4)
Specific Values (3)
Find the first positive minimum of WeierstrassP[x,1/2,1/2]:
WeierstrassP automatically evaluates to simpler functions for certain parameters:
Find a few singular points of WeierstrassP[x,{1/2,1/2}]:
Visualization (2)
Plot the WeierstrassP function for various parameters:
Function Properties (10)
Real domain of WeierstrassP:
WeierstrassP is an even function with respect to x:
WeierstrassP threads elementwise over lists in its first argument:
is not an analytic function of
:
It has both singularities and discontinuities:
is neither nondecreasing nor nonincreasing:
is neither non-negative nor non-positive:
is neither convex nor concave:
TraditionalForm formatting:
Differentiation (2)
Integration (3)
Compute the indefinite integral using Integrate:
Series Expansions (2)
Find the Taylor expansion using Series:
Applications (3)
Express roots of a cubic through WeierstrassP:
Uniformization of a generic elliptic curve :
The parametrized uniformization:
Check the correctness of the uniformization:
Special solution of the Korteweg–de Vries equation:
The Korteweg–de Vries equation:
Properties & Relations (5)
Integrate expressions involving WeierstrassP:
WeierstrassP is closely related to the EllipticExp function:
WeierstrassP is periodic, with periods equal to twice the half-periods:
WeierstrassP values at its half-periods:
Possible Issues (1)
Text
Wolfram Research (1988), WeierstrassP, Wolfram Language function, https://reference.wolfram.com/language/ref/WeierstrassP.html (updated 1996).
CMS
Wolfram Language. 1988. "WeierstrassP." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 1996. https://reference.wolfram.com/language/ref/WeierstrassP.html.
APA
Wolfram Language. (1988). WeierstrassP. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/WeierstrassP.html