InverseJacobiDS
✖
InverseJacobiDS
Details
- Mathematical function, suitable for both symbolic and numerical manipulation.
- gives the value of for which .
- InverseJacobiDS 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, InverseJacobiDS automatically evaluates to exact values.
- InverseJacobiDS can be evaluated to arbitrary numerical precision.
- InverseJacobiDS automatically threads over lists.
Examples
open allclose allBasic Examples (4)Summary of the most common use cases
https://wolfram.com/xid/0b0k1u1c4qy-hgzf1e
https://wolfram.com/xid/0b0k1u1c4qy-t2t97
Plot the function over a subset of the reals:
https://wolfram.com/xid/0b0k1u1c4qy-h2zjpq
Plot over a subset of the complexes:
https://wolfram.com/xid/0b0k1u1c4qy-kiedlx
Series expansion at the origin:
https://wolfram.com/xid/0b0k1u1c4qy-x4oml
Scope (31)Survey of the scope of standard use cases
Numerical Evaluation (5)
https://wolfram.com/xid/0b0k1u1c4qy-omcva4
The precision of the input tracks the precision of the output:
https://wolfram.com/xid/0b0k1u1c4qy-kq0cyt
Evaluate for complex arguments:
https://wolfram.com/xid/0b0k1u1c4qy-eosze0
Evaluate InverseJacobiDS efficiently at high precision:
https://wolfram.com/xid/0b0k1u1c4qy-di5gcr
https://wolfram.com/xid/0b0k1u1c4qy-bq2c6r
Compute average-case statistical intervals using Around:
https://wolfram.com/xid/0b0k1u1c4qy-cw18bq
Compute the elementwise values of an array:
https://wolfram.com/xid/0b0k1u1c4qy-thgd2
Or compute the matrix InverseJacobiDS function using MatrixFunction:
https://wolfram.com/xid/0b0k1u1c4qy-o5jpo
Specific Values (5)
Simple exact results are generated automatically:
https://wolfram.com/xid/0b0k1u1c4qy-kh2zre
Limiting values at the origin:
https://wolfram.com/xid/0b0k1u1c4qy-f0op35
https://wolfram.com/xid/0b0k1u1c4qy-kwzu4s
Find a real root of the equation :
https://wolfram.com/xid/0b0k1u1c4qy-f2hrld
https://wolfram.com/xid/0b0k1u1c4qy-kk6q9
Parity transformation is automatically applied:
https://wolfram.com/xid/0b0k1u1c4qy-io68q5
Visualization (3)
Plot InverseJacobiDS for various values of the second parameter :
https://wolfram.com/xid/0b0k1u1c4qy-ecj8m7
Plot InverseJacobiDS as a function of its parameter :
https://wolfram.com/xid/0b0k1u1c4qy-du62z6
https://wolfram.com/xid/0b0k1u1c4qy-bsucaf
https://wolfram.com/xid/0b0k1u1c4qy-7zbpb
Function Properties (6)
InverseJacobiDS is not an analytic function:
https://wolfram.com/xid/0b0k1u1c4qy-h5x4l2
It has both singularities and discontinuities:
https://wolfram.com/xid/0b0k1u1c4qy-mdtl3h
https://wolfram.com/xid/0b0k1u1c4qy-mn5jws
is neither nondecreasing nor nonincreasing:
https://wolfram.com/xid/0b0k1u1c4qy-nlz7s
https://wolfram.com/xid/0b0k1u1c4qy-xuztct
https://wolfram.com/xid/0b0k1u1c4qy-ctca0g
https://wolfram.com/xid/0b0k1u1c4qy-wc6uyg
https://wolfram.com/xid/0b0k1u1c4qy-oik3be
is neither non-negative nor non-positive:
https://wolfram.com/xid/0b0k1u1c4qy-84dui
is neither convex nor concave:
https://wolfram.com/xid/0b0k1u1c4qy-8kku21
Differentiation and Integration (5)
https://wolfram.com/xid/0b0k1u1c4qy-gn1a0i
https://wolfram.com/xid/0b0k1u1c4qy-nfbe0l
https://wolfram.com/xid/0b0k1u1c4qy-fxwmfc
Differentiate InverseJacobiDS with respect to the second argument :
https://wolfram.com/xid/0b0k1u1c4qy-jvw4u7
https://wolfram.com/xid/0b0k1u1c4qy-d48vi8
Definite integral of an odd function over an interval centered at the origin is 0:
https://wolfram.com/xid/0b0k1u1c4qy-mwfxq
Series Expansions (3)
https://wolfram.com/xid/0b0k1u1c4qy-ewr1h8
Plot the first three approximations for around :
https://wolfram.com/xid/0b0k1u1c4qy-binhar
https://wolfram.com/xid/0b0k1u1c4qy-c7itxf
Plot the first three approximations for around :
https://wolfram.com/xid/0b0k1u1c4qy-jkkunh
InverseJacobiDS can be applied to a power series:
https://wolfram.com/xid/0b0k1u1c4qy-i086bl
Function Identities and Simplifications (2)
InverseJacobiDS is the inverse function of JacobiDS:
https://wolfram.com/xid/0b0k1u1c4qy-v8ak2
Compose with inverse function:
https://wolfram.com/xid/0b0k1u1c4qy-b9xghn
Use PowerExpand to disregard multivaluedness of the inverse function:
https://wolfram.com/xid/0b0k1u1c4qy-bpvs1c
Other Features (2)
InverseJacobiDS threads elementwise over lists:
https://wolfram.com/xid/0b0k1u1c4qy-dj68j6
TraditionalForm formatting:
https://wolfram.com/xid/0b0k1u1c4qy-bw9j78
Applications (1)Sample problems that can be solved with this function
Properties & Relations (1)Properties of the function, and connections to other functions
Obtain InverseJacobiDS from solving equations containing elliptic functions:
https://wolfram.com/xid/0b0k1u1c4qy-jgo7zu
Wolfram Research (1988), InverseJacobiDS, Wolfram Language function, https://reference.wolfram.com/language/ref/InverseJacobiDS.html.
Text
Wolfram Research (1988), InverseJacobiDS, Wolfram Language function, https://reference.wolfram.com/language/ref/InverseJacobiDS.html.
Wolfram Research (1988), InverseJacobiDS, Wolfram Language function, https://reference.wolfram.com/language/ref/InverseJacobiDS.html.
CMS
Wolfram Language. 1988. "InverseJacobiDS." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/InverseJacobiDS.html.
Wolfram Language. 1988. "InverseJacobiDS." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/InverseJacobiDS.html.
APA
Wolfram Language. (1988). InverseJacobiDS. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/InverseJacobiDS.html
Wolfram Language. (1988). InverseJacobiDS. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/InverseJacobiDS.html
BibTeX
@misc{reference.wolfram_2024_inversejacobids, author="Wolfram Research", title="{InverseJacobiDS}", year="1988", howpublished="\url{https://reference.wolfram.com/language/ref/InverseJacobiDS.html}", note=[Accessed: 05-January-2025
]}
BibLaTeX
@online{reference.wolfram_2024_inversejacobids, organization={Wolfram Research}, title={InverseJacobiDS}, year={1988}, url={https://reference.wolfram.com/language/ref/InverseJacobiDS.html}, note=[Accessed: 05-January-2025
]}