WOLFRAM

Wolfram Language & System Documentation Center

InverseWeierstrassP[p,{g2,g3}]

gives a value of u for which the Weierstrass function is equal to p.

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Numerical Evaluation  
Specific Values  
Visualization  
Show More Show More
Function Properties  
Differentiation  
Integration  
Series Expansions  
Generalizations & Extensions  
Applications  
Properties & Relations  
Possible Issues  
See Also
Tech Notes
Related Guides
Related Links
History
Cite this Page

InverseWeierstrassP

InverseWeierstrassP[p,{g2,g3}]

gives a value of u for which the Weierstrass function is equal to p.

Details

  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • The value of u returned always lies in the fundamental period parallelogram defined by the complex half‐periods and .
  • InverseWeierstrassP[{p,q},{g2,g3}] finds the unique value of u for which and . For such a value to exist, p and q must be related by .
  • InverseWeierstrassP can be evaluated to arbitrary numerical precision.

Examples

open all close all

Basic Examples  (4)

Evaluate numerically:

Plot over a subset of the reals:

Plot over a subset of the complexes:

Series expansion at the origin:

Scope  (20)

Numerical Evaluation  (4)

Evaluate numerically:

Evaluate to high precision:

The precision of the output tracks the precision of the input:

Complex number input:

Evaluate efficiently at high precision:

Specific Values  (4)

Values at fixed points:

Value at zero:

Find a value of x for which InverseWeierstrassP[x,{1,2}]=2:

TraditionalForm formatting:

Visualization  (2)

Plot the InverseWeierstrassP function for various parameters:

Plot the real part of TemplateBox[{z, 7, 1}, InverseWeierstrassP]:

Plot the imaginary part of TemplateBox[{z, 7, 1}, InverseWeierstrassP]:

Function Properties  (4)

InverseWeierstrassP has both singularities and discontinuities:

TemplateBox[{x, 1, 2}, InverseWeierstrassP] is injective:

TemplateBox[{x, 1, 2}, InverseWeierstrassP] is neither non-negative nor non-positive:

It is complex-valued over part of the real axis

TemplateBox[{x, {1, /, 2}, {1, /, 2}}, InverseWeierstrassP] is neither convex nor concave:

It is complex-valued over part of the real axis:

Differentiation  (2)

First derivative with respect to :

Higher derivatives with respect to :

Plot the higher derivatives with respect to when and :

Integration  (2)

Compute the indefinite integral using Integrate:

Verify the antiderivative:

Definite integral:

Series Expansions  (2)

Find the Taylor expansion using Series:

Plots of the first three approximations around :

Taylor expansion at a generic point:

Generalizations & Extensions  (1)

Evaluate the generalized form numerically:

These are the inverse relationships with WeierstrassP and WeierstrassPPrime:

Applications  (2)

Plot the real and imaginary part of InverseWeierstrassP:

Form derivatives:

Properties & Relations  (1)

InverseWeierstrassP is closely related to EllipticLog function:

Evaluate numerically:

Compare with the value of the built-in function:

Possible Issues  (2)

If the first argument does not represent a pair of values of Weierstrass functions, InverseWeierstrassP stays unevaluated:

InverseWeierstrassP evaluates to a vector‐valued first argument:

Wolfram Research (1996), InverseWeierstrassP, Wolfram Language function, https://reference.wolfram.com/language/ref/InverseWeierstrassP.html.

Text

Wolfram Research (1996), InverseWeierstrassP, Wolfram Language function, https://reference.wolfram.com/language/ref/InverseWeierstrassP.html.

CMS

Wolfram Language. 1996. "InverseWeierstrassP." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/InverseWeierstrassP.html.

APA

Wolfram Language. (1996). InverseWeierstrassP. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/InverseWeierstrassP.html

BibTeX

@misc{reference.wolfram_2025_inverseweierstrassp, author="Wolfram Research", title="{InverseWeierstrassP}", year="1996", howpublished="\url{https://reference.wolfram.com/language/ref/InverseWeierstrassP.html}", note=[Accessed: 13-August-2025]}

BibLaTeX

@online{reference.wolfram_2025_inverseweierstrassp, organization={Wolfram Research}, title={InverseWeierstrassP}, year={1996}, url={https://reference.wolfram.com/language/ref/InverseWeierstrassP.html}, note=[Accessed: 13-August-2025]}