InverseJacobiNC

Notations

Traditional name

Traditional notation

Mathematica StandardForm notation

Primary definition

Specific values

Specialized values

For fixed z

For fixed m

Values at infinities

General characteristics

Domain and analyticity

(nc^(-1))(z|m) is an analytical function of z and m which is defined over (ℂ^2).

Symmetries and periodicities

Mirror symmetry

Quasi-reflection symmetry

Poles and essential singularities

With respect to m

The function (nc^(-1))(z|m) does not have poles and essential singularities with respect to m.

With respect to z

The function (nc^(-1))(z|m) does not have poles and essential singularities with respect to z.

Branch points

With respect to m

With respect to z

Branch cuts

Branch cut locations: complicated

Series representations

Generalized power series

Expansions at z==0

Expansions at m==0

Integral representations

On the real axis

Of the direct function

Differential equations

Ordinary nonlinear differential equations

Transformations

Transformations and argument simplifications

Argument involving basic arithmetic operations

Identities

Functional identities

Differentiation

Low-order differentiation

With respect to z

With respect to m

Symbolic differentiation

With respect to z

With respect to m

Fractional integro-differentiation

With respect to z

With respect to m

Integration

Indefinite integration

Involving only one direct function

Involving only one direct function with respect to m

Representations through more general functions

Through hypergeometric functions of two variables

Through other functions

Involving some hypergeometric-type functions

Representations through equivalent functions

With inverse function

With related functions

Involving InverseJacobiCD

Involving InverseJacobiCN

Involving InverseJacobiCS

Involving InverseJacobiDC

Involving InverseJacobiDN

Involving InverseJacobiDS

Involving InverseJacobiND

Involving InverseJacobiNS

Involving InverseJacobiSC

Involving InverseJacobiSD

Involving InverseJacobiSN

Involving elliptic integrals

Involving other related functions

History

– N. H. Abel (1826)
– A. G. Greenhill (1892)
– L. M. Milne–Thompson (1948)

Copyright