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   http://functions.wolfram.com/06.28.06.0017.01
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    Erfi[z] \[Proportional] Piecewise[{{-I + E^z^2/(Sqrt[Pi] z), Arg[z] <= 0}}, 
   I + E^z^2/(Sqrt[Pi] z)] /; (Abs[z] -> Infinity) 
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   Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Erfi", "[", "z", "]"]], "\[Proportional]", RowBox[List["Piecewise", "[", RowBox[List[RowBox[List["{", RowBox[List["{", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], "+", FractionBox[SuperscriptBox["\[ExponentialE]", SuperscriptBox["z", "2"]], RowBox[List[SqrtBox["\[Pi]"], " ", "z"]]]]], ",", RowBox[List[RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", "0"]]]], "}"]], "}"]], ",", RowBox[List["\[ImaginaryI]", "+", FractionBox[SuperscriptBox["\[ExponentialE]", SuperscriptBox["z", "2"]], RowBox[List[SqrtBox["\[Pi]"], " ", "z"]]]]]]], "]"]]]], "/;", RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Rule]", "\[Infinity]"]], ")"]]]]]] 
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   <math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'>  <semantics>  <mrow>  <mrow>  <mrow>  <mi> erfi </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mi> z </mi>  <mo> ) </mo>  </mrow>  <mo> ∝ </mo>  <mrow>  <mo>  </mo>  <mtable>  <mtr>  <mtd>  <mrow>  <mrow>  <mo> - </mo>  <mi> ⅈ </mi>  </mrow>  <mo> + </mo>  <mfrac>  <msup>  <mi> ⅇ </mi>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  </msup>  <mrow>  <msqrt>  <mi> π </mi>  </msqrt>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  </mfrac>  </mrow>  </mtd>  <mtd>  <mrow>  <mrow>  <mi> arg </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mi> z </mi>  <mo> ) </mo>  </mrow>  <mo> ≤ </mo>  <mn> 0 </mn>  </mrow>  </mtd>  </mtr>  <mtr>  <mtd>  <mrow>  <mi> ⅈ </mi>  <mo> + </mo>  <mfrac>  <msup>  <mi> ⅇ </mi>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  </msup>  <mrow>  <msqrt>  <mi> π </mi>  </msqrt>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  </mfrac>  </mrow>  </mtd>  <mtd>  <semantics>  <mi> True </mi>  <annotation encoding='Mathematica'> TagBox["True", "PiecewiseDefault", Rule[AutoDelete, False], Rule[DeletionWarning, True]] </annotation>  </semantics>  </mtd>  </mtr>  </mtable>  </mrow>  </mrow>  <mo> /; </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <semantics>  <mo> ❘ </mo>  <annotation encoding='Mathematica'> "\[LeftBracketingBar]" </annotation>  </semantics>  <mi> z </mi>  <semantics>  <mo> ❘ </mo>  <annotation encoding='Mathematica'> "\[RightBracketingBar]" </annotation>  </semantics>  </mrow>  <semantics>  <mo> → </mo>  <annotation encoding='Mathematica'> "\[Rule]" </annotation>  </semantics>  <mi> ∞ </mi>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <annotation-xml encoding='MathML-Content'>  <apply>  <ci> Condition </ci>  <apply>  <ci> Proportional </ci>  <apply>  <ci> Erfi </ci>  <ci> z </ci>  </apply>  <piecewise>  <piece>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> -1 </cn>  <imaginaryi />  </apply>  <apply>  <times />  <apply>  <power />  <exponentiale />  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  <apply>  <power />  <apply>  <times />  <apply>  <power />  <pi />  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <ci> z </ci>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  <apply>  <leq />  <apply>  <arg />  <ci> z </ci>  </apply>  <cn type='integer'> 0 </cn>  </apply>  </piece>  <otherwise>  <apply>  <plus />  <imaginaryi />  <apply>  <times />  <apply>  <power />  <exponentiale />  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  <apply>  <power />  <apply>  <times />  <apply>  <power />  <pi />  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <ci> z </ci>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  </otherwise>  </piecewise>  </apply>  <apply>  <ci> Rule </ci>  <apply>  <abs />  <ci> z </ci>  </apply>  <infinity />  </apply>  </apply>  </annotation-xml>  </semantics>  </math> 
   
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  | Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Erfi", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["\[Piecewise]", GridBox[List[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], "+", FractionBox[SuperscriptBox["\[ExponentialE]", SuperscriptBox["z", "2"]], RowBox[List[SqrtBox["\[Pi]"], " ", "z"]]]]], RowBox[List[RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", "0"]]], List[RowBox[List["\[ImaginaryI]", "+", FractionBox[SuperscriptBox["\[ExponentialE]", SuperscriptBox["z", "2"]], RowBox[List[SqrtBox["\[Pi]"], " ", "z"]]]]], TagBox["True", "PiecewiseDefault", Rule[AutoDelete, False], Rule[DeletionWarning, True]]]], Rule[ColumnAlignments, List[Left]], Rule[ColumnSpacings, 1.2`], Rule[ColumnWidths, Automatic]]]], "/;", RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Rule]", "\[Infinity]"]], ")"]]]]]]]]  |  
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   Date Added to functions.wolfram.com (modification date)
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