Erf2

Notations

Traditional name

Traditional notation

Mathematica StandardForm notation

Primary definition

Specific values

Specialized values

Values at fixed points

Values at infinities

General characteristics

Domain and analyticity

erf((Subscript[z, 1]),(Subscript[z, 2])) is an analytical function of (Subscript[z, 1])and (Subscript[z, 2])which is defined in (ℂ^2). For fixed (Subscript[z, 1])it is an entire function of (Subscript[z, 2]). For fixed (Subscript[z, 2])it is an entire function of (Subscript[z, 1]).

Symmetries and periodicities

Parity

erf((Subscript[z, 1]),(Subscript[z, 2])) is an odd function.

Mirror symmetry

Permutation symmetry

Periodicity

No periodicity

Poles and essential singularities

The function erf((Subscript[z, 1]),(Subscript[z, 2])) has singular points at (Subscript[z, 1])= (OverTilde[∞]) and (Subscript[z, 2])==(OverTilde[∞]).  They are essential singular points.

Branch points

The function erf((Subscript[z, 1]),(Subscript[z, 2])) does not have branch points.

Branch cuts

The function erf((Subscript[z, 1]),(Subscript[z, 2])) does not have branch cuts.

Series representations

Generalized power series

Expansions at {(Subscript[z, 1]),(Subscript[z, 2])}=={0,0}

Integral representations

On the real axis

Of the direct function

Differential equations

Ordinary linear differential equations and wronskians

For the direct function itself

Differentiation

Low-order differentiation

With respect to (Subscript[z, 1])

With respect to (Subscript[z, 2])

Symbolic differentiation

With respect to (Subscript[z, 1])

With respect to (Subscript[z, 2])

Fractional integro-differentiation

With respect to (Subscript[z, 1])

With respect to (Subscript[z, 2])

Integration

Indefinite integration

Involving only one direct function with respect to (Subscript[z, 1])

Involving one direct function and elementary functions with respect to (Subscript[z, 1])

Involving only one direct function with respect to (Subscript[z, 2])

Involving one direct function and elementary functions with respect to (Subscript[z, 2])

Representations through more general functions

Through hypergeometric functions

Involving Hypergeometric1F1

Involving hypergeometric HypergeometricU

Through Meijer G

Classical cases for the direct function itself

Generalized cases for the direct function itself

Through other functions

Representations through equivalent functions

With inverse function

Zeros

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