InverseJacobiSC [v,m]
gives the inverse Jacobi elliptic function .
InverseJacobiSC
InverseJacobiSC [v,m]
gives the inverse Jacobi elliptic function .
Details
- Mathematical function, suitable for both symbolic and numerical manipulation.
- gives the value of u for which .
- InverseJacobiSC has branch cut discontinuities in the complex v plane with branch points at and infinity, and in the complex m plane with branch points at and infinity.
- The inverse Jacobi elliptic functions are related to elliptic integrals.
- For certain special arguments, InverseJacobiSC automatically evaluates to exact values.
- InverseJacobiSC can be evaluated to arbitrary numerical precision.
- InverseJacobiSC automatically threads over lists.
Examples
open all close allBasic Examples (4)
Evaluate numerically:
Plot the function over a subset of the reals:
Plot over a subset of the complexes:
Series expansions at the origin:
Scope (29)
Numerical Evaluation (5)
Evaluate to high precision:
The precision of the output tracks the precision of the input:
Evaluate for complex arguments:
Evaluate InverseJacobiSC efficiently at high precision:
Compute average-case statistical intervals using Around :
Compute the elementwise values of an array:
Or compute the matrix InverseJacobiSC function using MatrixFunction :
Specific Values (4)
Simple exact results are generated automatically:
Values at infinity:
Find a real root of the equation TemplateBox[{x, {1, /, 3}}, InverseJacobiSC]=1:
Parity transformation is automatically applied:
Visualization (3)
Plot InverseJacobiSC for various values of the second parameter :
Plot InverseJacobiSC as a function of its parameter :
Plot the real part of TemplateBox[{z, 2}, InverseJacobiSC]:
Plot the imaginary part of TemplateBox[{z, 2}, InverseJacobiSC]:
Function Properties (6)
InverseJacobiSC is not an analytic function:
It has both singularities and discontinuities:
TemplateBox[{x, 3}, InverseJacobiSC] is nondecreasing on its real domain:
TemplateBox[{x, {1, /, 3}}, InverseJacobiSC] is injective:
TemplateBox[{x, 3}, InverseJacobiSC] is not surjective:
TemplateBox[{x, {1, /, 3}}, InverseJacobiSC] is neither non-negative nor non-positive:
TemplateBox[{x, {1, /, 3}}, InverseJacobiSC] is neither convex nor concave:
Differentiation and Integration (4)
First derivative:
Higher derivatives:
Plot higher derivatives for :
Differentiate InverseJacobiSC with respect to the second argument :
Definite integral of an odd function over an interval centered at the origin is 0:
Series Expansions (3)
Taylor expansion for TemplateBox[{nu, m}, InverseJacobiSC] around :
Plot the first three approximations for TemplateBox[{nu, 2}, InverseJacobiSC] around :
Taylor expansion for TemplateBox[{nu, m}, InverseJacobiSC] around :
Plot the first three approximations for TemplateBox[{nu, m}, InverseJacobiSC] around :
InverseJacobiSC can be applied to a power series:
Function Identities and Simplifications (2)
InverseJacobiSC is the inverse function of JacobiSC :
Compose with inverse function:
Use PowerExpand to disregard multivaluedness of the inverse function:
Other Features (2)
InverseJacobiSC threads elementwise over lists:
TraditionalForm formatting:
Applications (2)
Plot contours of constant real and imaginary parts in the complex plane:
Construct lowpass elliptic filter for analog signal:
Compute filter ripple parameters and associate elliptic function parameter:
Use elliptic degree equation to find the ratio of the pass and the stop frequencies:
Compute corresponding stop frequency and elliptic parameters:
Compute ripple locations and poles and zeros of the transfer function:
Compute poles of the transfer function:
Assemble the transfer function:
Compare with the result of EllipticFilterModel :
Properties & Relations (1)
Obtain InverseJacobiSC from solving equations containing elliptic functions:
Tech Notes
Related Guides
Related Links
History
Introduced in 1988 (1.0)
Text
Wolfram Research (1988), InverseJacobiSC, Wolfram Language function, https://reference.wolfram.com/language/ref/InverseJacobiSC.html.
CMS
Wolfram Language. 1988. "InverseJacobiSC." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/InverseJacobiSC.html.
APA
Wolfram Language. (1988). InverseJacobiSC. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/InverseJacobiSC.html
BibTeX
@misc{reference.wolfram_2025_inversejacobisc, author="Wolfram Research", title="{InverseJacobiSC}", year="1988", howpublished="\url{https://reference.wolfram.com/language/ref/InverseJacobiSC.html}", note=[Accessed: 16-November-2025]}
BibLaTeX
@online{reference.wolfram_2025_inversejacobisc, organization={Wolfram Research}, title={InverseJacobiSC}, year={1988}, url={https://reference.wolfram.com/language/ref/InverseJacobiSC.html}, note=[Accessed: 16-November-2025]}