Imaginary error function: Representations through equivalent functions (formula 06.28.27.0005)

Erfi

$Mathematica Notation$

Gamma, Beta, Erf

Erfi[z]

Representations through equivalent functions

With inverse function

http://functions.wolfram.com/06.28.27.0005.01

Input Form

Erfi[I InverseErfc[1 - z]] == I z

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["Erfi", "[", RowBox[List["\[ImaginaryI]", " ", RowBox[List["InverseErfc", "[", RowBox[List["1", "-", "z"]], "]"]]]], "]"]], "\[Equal]", RowBox[List["\[ImaginaryI]", " ", "z"]]]]]]

MathML Form

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mi> erfi </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <msup> <mi> erfc </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Erfi </ci> <apply> <times /> <imaginaryi /> <apply> <ci> InverseErfc </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <imaginaryi /> <ci> z </ci> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Erfi", "[", RowBox[List["\[ImaginaryI]", " ", RowBox[List["InverseErfc", "[", RowBox[List["1", "-", "z_"]], "]"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["\[ImaginaryI]", " ", "z"]]]]]]

Date Added to functions.wolfram.com (modification date)

2007-05-02