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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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