InverseJacobiSC
✖
InverseJacobiSC
Details

- Mathematical function, suitable for both symbolic and numerical manipulation.
gives the value of
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 allclose allBasic Examples (4)Summary of the most common use cases

https://wolfram.com/xid/05fn2ntpd6-csnrfu


https://wolfram.com/xid/05fn2ntpd6-fozy90

Plot the function over a subset of the reals:

https://wolfram.com/xid/05fn2ntpd6-cl8z6n

Plot over a subset of the complexes:

https://wolfram.com/xid/05fn2ntpd6-kiedlx

Series expansions at the origin:

https://wolfram.com/xid/05fn2ntpd6-k0am2i


https://wolfram.com/xid/05fn2ntpd6-haoeo4

Scope (29)Survey of the scope of standard use cases
Numerical Evaluation (5)

https://wolfram.com/xid/05fn2ntpd6-cu7ajp

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

https://wolfram.com/xid/05fn2ntpd6-bebro1

Evaluate for complex arguments:

https://wolfram.com/xid/05fn2ntpd6-el5vg8

Evaluate InverseJacobiSC efficiently at high precision:

https://wolfram.com/xid/05fn2ntpd6-di5gcr


https://wolfram.com/xid/05fn2ntpd6-bq2c6r

Compute average-case statistical intervals using Around:

https://wolfram.com/xid/05fn2ntpd6-cw18bq

Compute the elementwise values of an array:

https://wolfram.com/xid/05fn2ntpd6-thgd2

Or compute the matrix InverseJacobiSC function using MatrixFunction:

https://wolfram.com/xid/05fn2ntpd6-o5jpo

Specific Values (4)
Simple exact results are generated automatically:

https://wolfram.com/xid/05fn2ntpd6-mp1qb


https://wolfram.com/xid/05fn2ntpd6-dsfiq2


https://wolfram.com/xid/05fn2ntpd6-fgzzd3


https://wolfram.com/xid/05fn2ntpd6-bd1o7y

Find a real root of the equation :

https://wolfram.com/xid/05fn2ntpd6-f2hrld


https://wolfram.com/xid/05fn2ntpd6-g0p9bp

Parity transformation is automatically applied:

https://wolfram.com/xid/05fn2ntpd6-io68q5

Visualization (3)
Plot InverseJacobiSC for various values of the second parameter :

https://wolfram.com/xid/05fn2ntpd6-ecj8m7

Plot InverseJacobiSC as a function of its parameter :

https://wolfram.com/xid/05fn2ntpd6-du62z6


https://wolfram.com/xid/05fn2ntpd6-bsucaf


https://wolfram.com/xid/05fn2ntpd6-i394yp

Function Properties (6)
InverseJacobiSC is not an analytic function:

https://wolfram.com/xid/05fn2ntpd6-czmfmr

It has both singularities and discontinuities:

https://wolfram.com/xid/05fn2ntpd6-xpyfx6


https://wolfram.com/xid/05fn2ntpd6-y49d8q

is nondecreasing on its real domain:

https://wolfram.com/xid/05fn2ntpd6-tz1xij


https://wolfram.com/xid/05fn2ntpd6-poz8g


https://wolfram.com/xid/05fn2ntpd6-ctca0g


https://wolfram.com/xid/05fn2ntpd6-kojhy0


https://wolfram.com/xid/05fn2ntpd6-hdm869

is neither non-negative nor non-positive:

https://wolfram.com/xid/05fn2ntpd6-84dui

is neither convex nor concave:

https://wolfram.com/xid/05fn2ntpd6-8kku21

Differentiation and Integration (4)

https://wolfram.com/xid/05fn2ntpd6-gn1a0i


https://wolfram.com/xid/05fn2ntpd6-nfbe0l


https://wolfram.com/xid/05fn2ntpd6-fxwmfc

Differentiate InverseJacobiSC with respect to the second argument :

https://wolfram.com/xid/05fn2ntpd6-jvw4u7

Definite integral of an odd function over an interval centered at the origin is 0:

https://wolfram.com/xid/05fn2ntpd6-mwfxq

Series Expansions (3)

https://wolfram.com/xid/05fn2ntpd6-ewr1h8

Plot the first three approximations for around
:

https://wolfram.com/xid/05fn2ntpd6-binhar


https://wolfram.com/xid/05fn2ntpd6-c7itxf

Plot the first three approximations for around
:

https://wolfram.com/xid/05fn2ntpd6-jkkunh

InverseJacobiSC can be applied to a power series:

https://wolfram.com/xid/05fn2ntpd6-bkeep9

Function Identities and Simplifications (2)
InverseJacobiSC is the inverse function of JacobiSC:

https://wolfram.com/xid/05fn2ntpd6-v8ak2

Compose with inverse function:

https://wolfram.com/xid/05fn2ntpd6-cnjroa

Use PowerExpand to disregard multivaluedness of the inverse function:

https://wolfram.com/xid/05fn2ntpd6-7tz5

Other Features (2)
InverseJacobiSC threads elementwise over lists:

https://wolfram.com/xid/05fn2ntpd6-hqxkna

TraditionalForm formatting:

https://wolfram.com/xid/05fn2ntpd6-c9dwzb

Applications (2)Sample problems that can be solved with this function
Plot contours of constant real and imaginary parts in the complex plane:

https://wolfram.com/xid/05fn2ntpd6-yu4ti

Construct lowpass elliptic filter for analog signal:

https://wolfram.com/xid/05fn2ntpd6-bxw8jc
Compute filter ripple parameters and associate elliptic function parameter:

https://wolfram.com/xid/05fn2ntpd6-bm1kjg
Use elliptic degree equation to find the ratio of the pass and the stop frequencies:

https://wolfram.com/xid/05fn2ntpd6-b13u0f

Compute corresponding stop frequency and elliptic parameters:

https://wolfram.com/xid/05fn2ntpd6-wtjxg

Compute ripple locations and poles and zeros of the transfer function:

https://wolfram.com/xid/05fn2ntpd6-kvrem
Compute poles of the transfer function:

https://wolfram.com/xid/05fn2ntpd6-elkxl1
Assemble the transfer function:

https://wolfram.com/xid/05fn2ntpd6-fyal2v

https://wolfram.com/xid/05fn2ntpd6-bv4lrk

Compare with the result of EllipticFilterModel:

https://wolfram.com/xid/05fn2ntpd6-00j7s

https://wolfram.com/xid/05fn2ntpd6-ef2b35

Properties & Relations (1)Properties of the function, and connections to other functions
Obtain InverseJacobiSC from solving equations containing elliptic functions:

https://wolfram.com/xid/05fn2ntpd6-jgo7zu


Wolfram Research (1988), InverseJacobiSC, Wolfram Language function, https://reference.wolfram.com/language/ref/InverseJacobiSC.html.
Text
Wolfram Research (1988), InverseJacobiSC, Wolfram Language function, https://reference.wolfram.com/language/ref/InverseJacobiSC.html.
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.
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
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: 06-June-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: 06-June-2025
]}