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Notations

Traditional name

Traditional notation

Mathematica StandardForm notation

Primary definition

Specific values

Specialized values

General characteristics

Domain and analyticity

(Subscript[W, k])(z) is an analytical function of z which is defined over ℂ.

Symmetries and periodicities

Periodicity

No periodicity

Poles and essential singularities

With respect to z

The function (Subscript[W, k])(z) does not have poles and essential singularities.

Branch points

With respect to z

Branch cuts

With respect to z

The function (Subscript[W, k])(z), k≠0, is a single-valued function on the z-plane cut along the interval (-∞, 0), where it is continuous from above.

Series representations

Asymptotic series expansions

Integral representations

On the real axis

Of the direct function

Limit representations

Differential equations

Ordinary nonlinear differential equations

Identities

Functional identities

Differentiation

Low-order differentiation

Symbolic differentiation

Eric Weisstein and Oleg Marichev

Integration

Indefinite integration

Involving only one direct function

Involving one direct function and elementary functions

Representations through equivalent functions

With inverse function

With related functions

History

– J. H. Lambert (1758)
– L. Euler (1764, 1779)
- R. Corless, D. Knuth (1993)

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