InverseJacobiSN
InverseJacobiSN[v,m]
gives the inverse Jacobi elliptic function .
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)
Plot the function at different values of the modulus m:
Plot over a subset of the complexes:
Series expansions at the origin:
Series expansion at Infinity:
Scope (29)
Numerical Evaluation (5)
The precision of the input tracks the precision of the output:
Evaluate for complex arguments:
Evaluate InverseJacobiSN efficiently at high precision:
Compute average-case statistical intervals using Around:
Compute the elementwise values of an array:
Or compute the matrix InverseJacobiSN function using MatrixFunction:
Specific Values (4)
Visualization (3)
Plot InverseJacobiSN for various values of the second parameter :
Plot InverseJacobiSN as a function of its parameter :
Function Properties (6)
InverseJacobiSN is not an analytic function:
It has both singularities and discontinuities:
is nondecreasing on its real domain:
is neither non-negative nor non-positive on its real domain:
Differentiation and Integration (4)
Differentiate InverseJacobiSN with respect to the second argument :
Definite integral of an odd function over an interval centered at the origin is 0:
Series Expansions (2)
Function Identities and Simplifications (2)
InverseJacobiSN is the inverse function of JacobiSN:
Compose with inverse function:
Use PowerExpand to disregard multivaluedness of the inverse function:
Other Features (3)
InverseJacobiSN threads elementwise over lists:
InverseJacobiSN can be applied to a power series:
TraditionalForm formatting:
Generalizations & Extensions (1)
InverseJacobiSN can be applied to a power series:
Properties & Relations (1)
Obtain InverseJacobiSN from solving equations containing elliptic functions:
Text
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.
APA
Wolfram Language. (1988). InverseJacobiSN. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/InverseJacobiSN.html