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 | | http://functions.wolfram.com/06.28.06.0005.01 | 
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 | | Erfi[z] \[Proportional] z/Sqrt[-z^2] + (E^z^2/(Sqrt[Pi] z)) 
    HypergeometricPFQ[{1, 1/2}, {}, 1/z^2] /; (Abs[z] -> Infinity) | 
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 | | Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Erfi", "[", "z", "]"]], "\[Proportional]", RowBox[List[FractionBox[RowBox[List["z", " "]], RowBox[List[" ", SqrtBox[RowBox[List["-", SuperscriptBox["z", "2"]]]]]]], "+", RowBox[List[FractionBox[SuperscriptBox["\[ExponentialE]", SuperscriptBox["z", "2"]], RowBox[List[SqrtBox["\[Pi]"], " ", "z"]]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List["1", ",", FractionBox["1", "2"]]], "}"]], ",", RowBox[List["{", "}"]], ",", FractionBox["1", SuperscriptBox["z", "2"]]]], "]"]]]]]]]], "/;", 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>  <mfrac>  <mi> z </mi>  <msqrt>  <mrow>  <mo> - </mo>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  </mrow>  </msqrt>  </mfrac>  <mo> + </mo>  <mrow>  <mfrac>  <mn> 1 </mn>  <mrow>  <msqrt>  <mi> π </mi>  </msqrt>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  </mfrac>  <mo> ⁢ </mo>  <msup>  <mi> ⅇ </mi>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  </msup>  <mo> ⁢ </mo>  <semantics>  <mrow>  <mrow>  <msub>  <mo>   </mo>  <mn> 2 </mn>  </msub>  <msub>  <mi> F </mi>  <mn> 0 </mn>  </msub>  </mrow>  <mo> ⁡ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 1 </mn>  <mo> , </mo>  <mfrac>  <mn> 1 </mn>  <mn> 2 </mn>  </mfrac>  </mrow>  <mo> ; </mo>  <mo>   </mo>  <mo> ; </mo>  <mfrac>  <mn> 1 </mn>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  </mfrac>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["0", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["1", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox["1", "2"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox["\[Null]", InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[FractionBox["1", SuperscriptBox["z", "2"]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] </annotation>  </semantics>  </mrow>  </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>  <apply>  <plus />  <apply>  <times />  <ci> z </ci>  <apply>  <power />  <apply>  <power />  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <times />  <apply>  <times />  <cn type='integer'> 1 </cn>  <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>  <power />  <exponentiale />  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  <apply>  <ci> HypergeometricPFQ </ci>  <list>  <cn type='integer'> 1 </cn>  <cn type='rational'> 1 <sep /> 2 </cn>  </list>  <list />  <apply>  <times />  <cn type='integer'> 1 </cn>  <apply>  <power />  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  </apply>  </apply>  </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[FractionBox["z", SqrtBox[RowBox[List["-", SuperscriptBox["z", "2"]]]]], "+", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", SuperscriptBox["z", "2"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List["1", ",", FractionBox["1", "2"]]], "}"]], ",", RowBox[List["{", "}"]], ",", FractionBox["1", SuperscriptBox["z", "2"]]]], "]"]]]], RowBox[List[SqrtBox["\[Pi]"], " ", "z"]]]]], "/;", 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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