WeierstrassPPrime
WeierstrassPPrime[u,{g2,g3}]
gives the derivative of the Weierstrass elliptic function .
Details

- Mathematical function, suitable for both symbolic and numerical manipulation.
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- For certain special arguments, WeierstrassPPrime automatically evaluates to exact values.
- WeierstrassPPrime can be evaluated to arbitrary numerical precision.
Examples
open allclose allBasic Examples (4)
Scope (29)
Numerical Evaluation (4)
Specific Values (4)
Find a value of x for which WeierstrassPPrime[x,1/2,1/2]=10:
WeierstrassPPrime automatically evaluates to simpler functions for certain parameters:
Find a few singular points of WeierstrassPPrime[x,{1/2,1/2}]:
Visualization (2)
Plot the WeierstrassPPrime function for various parameters:
Function Properties (10)
Real domain of WeierstrassPPrime:
WeierstrassPPrime is an odd function with respect to x:
WeierstrassPPrime 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 (4)
Compute the indefinite integral using Integrate:
Definite integral of WeierstrassPPrime[z,{g2,g3}] over a period is 0:
Series Expansions (3)
Find the Taylor expansion using Series:
Plots of the first three approximations around :
Applications (4)
Conformal map from a triangle to the upper half‐plane:
Uniformization of a generic elliptic curve :
The parametrized uniformization:
Check the correctness of the uniformization:
Define Dixon trigonometric functions:
These functions are cubic generalizations of Cos and Sin:
Plot the Dixon trigonometric functions:
Properties & Relations (2)
Integrate expressions involving WeierstrassPPrime:
WeierstrassPPrime is closely related to EllipticExpPrime:
Possible Issues (1)
Text
Wolfram Research (1988), WeierstrassPPrime, Wolfram Language function, https://reference.wolfram.com/language/ref/WeierstrassPPrime.html (updated 1996).
CMS
Wolfram Language. 1988. "WeierstrassPPrime." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 1996. https://reference.wolfram.com/language/ref/WeierstrassPPrime.html.
APA
Wolfram Language. (1988). WeierstrassPPrime. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/WeierstrassPPrime.html