InverseJacobiSN
✖
InverseJacobiSN
Details

- Mathematical function, suitable for both symbolic and numerical manipulation.
gives the value of
for which
.
- InverseJacobiSN 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, InverseJacobiSN automatically evaluates to exact values.
- InverseJacobiSN can be evaluated to arbitrary numerical precision.
- InverseJacobiSN automatically threads over lists.
Examples
open allclose allBasic Examples (5)Summary of the most common use cases

https://wolfram.com/xid/05fn2ntpd0-meb4zz


https://wolfram.com/xid/05fn2ntpd0-fx5nu

Plot the function at different values of the modulus m:

https://wolfram.com/xid/05fn2ntpd0-gkapxz

Plot over a subset of the complexes:

https://wolfram.com/xid/05fn2ntpd0-kiedlx

Series expansions at the origin:

https://wolfram.com/xid/05fn2ntpd0-bb036u


https://wolfram.com/xid/05fn2ntpd0-h0yjtt

Series expansion at Infinity:

https://wolfram.com/xid/05fn2ntpd0-laddhh

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

https://wolfram.com/xid/05fn2ntpd0-omcva4

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

https://wolfram.com/xid/05fn2ntpd0-kq0cyt

Evaluate for complex arguments:

https://wolfram.com/xid/05fn2ntpd0-gwgca0

Evaluate InverseJacobiSN efficiently at high precision:

https://wolfram.com/xid/05fn2ntpd0-di5gcr


https://wolfram.com/xid/05fn2ntpd0-bq2c6r

Compute average-case statistical intervals using Around:

https://wolfram.com/xid/05fn2ntpd0-cw18bq

Compute the elementwise values of an array:

https://wolfram.com/xid/05fn2ntpd0-thgd2

Or compute the matrix InverseJacobiSN function using MatrixFunction:

https://wolfram.com/xid/05fn2ntpd0-o5jpo

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

https://wolfram.com/xid/05fn2ntpd0-kh2zre


https://wolfram.com/xid/05fn2ntpd0-k55w8c


https://wolfram.com/xid/05fn2ntpd0-i30i9x

Find a real root of the equation :

https://wolfram.com/xid/05fn2ntpd0-f2hrld


https://wolfram.com/xid/05fn2ntpd0-vf3cy

Parity transformation is automatically applied:

https://wolfram.com/xid/05fn2ntpd0-e30g5k

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

https://wolfram.com/xid/05fn2ntpd0-ecj8m7

Plot InverseJacobiSN as a function of its parameter :

https://wolfram.com/xid/05fn2ntpd0-du62z6


https://wolfram.com/xid/05fn2ntpd0-bsucaf


https://wolfram.com/xid/05fn2ntpd0-hghz57

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

https://wolfram.com/xid/05fn2ntpd0-h5x4l2

It has both singularities and discontinuities:

https://wolfram.com/xid/05fn2ntpd0-mdtl3h


https://wolfram.com/xid/05fn2ntpd0-mn5jws

is nondecreasing on its real domain:

https://wolfram.com/xid/05fn2ntpd0-h8qot7


https://wolfram.com/xid/05fn2ntpd0-poz8g


https://wolfram.com/xid/05fn2ntpd0-ctca0g


https://wolfram.com/xid/05fn2ntpd0-kojhy0


https://wolfram.com/xid/05fn2ntpd0-hdm869

is neither non-negative nor non-positive on its real domain:

https://wolfram.com/xid/05fn2ntpd0-84dui

is neither convex nor concave on its real domain:

https://wolfram.com/xid/05fn2ntpd0-t4i9j7

Differentiation and Integration (4)

https://wolfram.com/xid/05fn2ntpd0-gn1a0i


https://wolfram.com/xid/05fn2ntpd0-nfbe0l


https://wolfram.com/xid/05fn2ntpd0-fxwmfc

Differentiate InverseJacobiSN with respect to the second argument :

https://wolfram.com/xid/05fn2ntpd0-jvw4u7

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

https://wolfram.com/xid/05fn2ntpd0-mwfxq

Series Expansions (2)

https://wolfram.com/xid/05fn2ntpd0-ewr1h8

Plot the first three approximations for around
:

https://wolfram.com/xid/05fn2ntpd0-binhar


https://wolfram.com/xid/05fn2ntpd0-c7itxf

Plot the first three approximations for around
:

https://wolfram.com/xid/05fn2ntpd0-jkkunh

Function Identities and Simplifications (2)
InverseJacobiSN is the inverse function of JacobiSN:

https://wolfram.com/xid/05fn2ntpd0-v8ak2

Compose with inverse function:

https://wolfram.com/xid/05fn2ntpd0-x2iv5

Use PowerExpand to disregard multivaluedness of the inverse function:

https://wolfram.com/xid/05fn2ntpd0-gmtkil

Other Features (3)
InverseJacobiSN threads elementwise over lists:

https://wolfram.com/xid/05fn2ntpd0-ds2fki

InverseJacobiSN can be applied to a power series:

https://wolfram.com/xid/05fn2ntpd0-j653rg

TraditionalForm formatting:

https://wolfram.com/xid/05fn2ntpd0-c9dwzb

Generalizations & Extensions (1)Generalized and extended use cases
InverseJacobiSN can be applied to a power series:

https://wolfram.com/xid/05fn2ntpd0-bkeep9

Applications (1)Sample problems that can be solved with this function
Properties & Relations (1)Properties of the function, and connections to other functions
Obtain InverseJacobiSN from solving equations containing elliptic functions:

https://wolfram.com/xid/05fn2ntpd0-jgo7zu


Wolfram Research (1988), InverseJacobiSN, Wolfram Language function, https://reference.wolfram.com/language/ref/InverseJacobiSN.html.
Text
Wolfram Research (1988), InverseJacobiSN, Wolfram Language function, https://reference.wolfram.com/language/ref/InverseJacobiSN.html.
Wolfram Research (1988), InverseJacobiSN, Wolfram Language function, https://reference.wolfram.com/language/ref/InverseJacobiSN.html.
CMS
Wolfram Language. 1988. "InverseJacobiSN." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/InverseJacobiSN.html.
Wolfram Language. 1988. "InverseJacobiSN." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/InverseJacobiSN.html.
APA
Wolfram Language. (1988). InverseJacobiSN. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/InverseJacobiSN.html
Wolfram Language. (1988). InverseJacobiSN. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/InverseJacobiSN.html
BibTeX
@misc{reference.wolfram_2025_inversejacobisn, author="Wolfram Research", title="{InverseJacobiSN}", year="1988", howpublished="\url{https://reference.wolfram.com/language/ref/InverseJacobiSN.html}", note=[Accessed: 01-June-2025
]}
BibLaTeX
@online{reference.wolfram_2025_inversejacobisn, organization={Wolfram Research}, title={InverseJacobiSN}, year={1988}, url={https://reference.wolfram.com/language/ref/InverseJacobiSN.html}, note=[Accessed: 01-June-2025
]}