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Erfi




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Erfi[z] > Representations through more general functions > Through Meijer G > Classical cases for the direct function itself





http://functions.wolfram.com/06.28.26.0005.01









  


  








Input Form





Erfi[z] == (I/Sqrt[Pi]) MeijerG[{{1}, {}}, {{1/2}, {0}}, -z^2] /; Im[z] > 0








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Erfi", "[", "z", "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["\[ImaginaryI]", " "]], SqrtBox["\[Pi]"]], RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", "1", "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", FractionBox["1", "2"], "}"]], ",", RowBox[List["{", "0", "}"]]]], "}"]], ",", RowBox[List["-", SuperscriptBox["z", "2"]]]]], "]"]]]]]], "/;", RowBox[List[RowBox[List["Im", "[", "z", "]"]], ">", "0"]]]]]]








MathML Form







<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> &#8290; </mo> <mrow> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <mi> &#8520; </mi> <msqrt> <mi> &#960; </mi> </msqrt> </mfrac> <mo> &#8290; </mo> <semantics> <mrow> <msubsup> <mi> G </mi> <mrow> <mn> 1 </mn> <mo> , </mo> <mn> 2 </mn> </mrow> <mrow> <mn> 1 </mn> <mo> , </mo> <mn> 1 </mn> </mrow> </msubsup> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> &#10072; </mo> <mtable> <mtr> <mtd> <mn> 1 </mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> , </mo> <mn> 0 </mn> </mrow> </mtd> </mtr> </mtable> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubsuperscriptBox[TagBox[&quot;G&quot;, MeijerG], RowBox[List[&quot;1&quot;, &quot;,&quot;, &quot;2&quot;]], RowBox[List[&quot;1&quot;, &quot;,&quot;, &quot;1&quot;]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[RowBox[List[&quot;-&quot;, SuperscriptBox[&quot;z&quot;, &quot;2&quot;]]], MeijerG, Rule[Editable, True]], &quot;\[VerticalSeparator]&quot;, GridBox[List[List[TagBox[&quot;1&quot;, MeijerG, Rule[Editable, True]]], List[RowBox[List[TagBox[FractionBox[&quot;1&quot;, &quot;2&quot;], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;0&quot;, MeijerG, Rule[Editable, True]]]]]]]]], &quot;)&quot;]]]], MeijerG, Rule[Editable, False]] </annotation> </semantics> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> Im </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> &gt; </mo> <mn> 0 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <times /> <ci> erfi </ci> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <imaginaryi /> <apply> <power /> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> MeijerG </ci> <list> <list> <cn type='integer'> 1 </cn> </list> <list /> </list> <list> <list> <cn type='rational'> 1 <sep /> 2 </cn> </list> <list> <cn type='integer'> 0 </cn> </list> </list> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <gt /> <apply> <times /> <imaginary /> <ci> z </ci> </apply> <cn type='integer'> 0 </cn> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Erfi", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", "1", "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", FractionBox["1", "2"], "}"]], ",", RowBox[List["{", "0", "}"]]]], "}"]], ",", RowBox[List["-", SuperscriptBox["z", "2"]]]]], "]"]]]], SqrtBox["\[Pi]"]], "/;", RowBox[List[RowBox[List["Im", "[", "z", "]"]], ">", "0"]]]]]]]]


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





2001-10-29