EllipticLog

Notations

Traditional name

Traditional notation

Mathematica StandardForm notation

Primary definition

General characteristics

Domain and analyticity

elog((Subscript[z, 1]),(Subscript[z, 2]);a,b) is an analytical function of (Subscript[z, 1]), (Subscript[z, 2]), a, b, which is defined in (ℂ^4).

Symmetries and periodicities

Mirror symmetry

Periodicity

No periodicity

Poles and essential singularities

The function elog((Subscript[z, 1]),(Subscript[z, 2]);a,b) does not have poles and essential singularities.

Branch points

Branch points locations: complicated

Branch cuts

Branch cut locations: complicated

Integral representations

On the real axis

Of the direct function

Differential equations

Ordinary linear differential equations and wronskians

For the direct function itself

Ordinary nonlinear differential equations

Differentiation

Low-order differentiation

With respect to (Subscript[z,  1])

Representations through more general functions

Through other functions

Involving some hypergeometric-type functions

Representations through equivalent functions

With inverse function

With related functions

Involving Weierstrass functions

Involving incomplete elliptic integrals

History

– D. Masser (1975)

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