Imaginary error function: Series representations (formula 06.28.06.0015)

Erfi

$Mathematica Notation$

Gamma, Beta, Erf

Erfi[z]

Series representations

Generalized power series

Expansions at z==0

For the function itself

http://functions.wolfram.com/06.28.06.0015.01

Input Form

Erfi[z] \[Proportional] (2/Sqrt[Pi]) (z + z^3/3 + z^5/10 + O[z^7])

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["Erfi", "[", "z", "]"]], "\[Proportional]", RowBox[List[FractionBox["2", SqrtBox["\[Pi]"]], RowBox[List["(", RowBox[List["z", "+", FractionBox[SuperscriptBox["z", "3"], "3"], "+", FractionBox[SuperscriptBox["z", "5"], "10"], "+", RowBox[List["O", "[", SuperscriptBox["z", "7"], "]"]]]], ")"]]]]]]]]

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> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ∝ </mo> <mrow> <mfrac> <mn> 2 </mn> <msqrt> <mi> π </mi> </msqrt> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mfrac> <msup> <mi> z </mi> <mn> 3 </mn> </msup> <mn> 3 </mn> </mfrac> <mo> + </mo> <mfrac> <msup> <mi> z </mi> <mn> 5 </mn> </msup> <mn> 10 </mn> </mfrac> <mo> + </mo> <mrow> <mi> O </mi> <mo> ⁡ </mo> <mo> ( </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Proportional </ci> <apply> <ci> Erfi </ci> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <ci> z </ci> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> <apply> <power /> <cn type='integer'> 10 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> O </ci> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Erfi", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List["z", "+", FractionBox[SuperscriptBox["z", "3"], "3"], "+", FractionBox[SuperscriptBox["z", "5"], "10"], "+", SuperscriptBox[RowBox[List["O", "[", "z", "]"]], "7"]]], ")"]]]], SqrtBox["\[Pi]"]]]]]]

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

2007-05-02