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Erfi




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Erfi[z] > Series representations > Generalized power series > Expansions at generic point z==z0 > For the function itself





http://functions.wolfram.com/06.28.06.0011.01









  


  








Input Form





Erfi[z] \[Proportional] Erfi[Subscript[z, 0]] + ((2 E^Subscript[z, 0]^2)/Sqrt[Pi]) (z - Subscript[z, 0]) + ((2 E^Subscript[z, 0]^2 Subscript[z, 0])/Sqrt[Pi]) (z - Subscript[z, 0])^2 + O[(z - Subscript[z, 0])^3]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Erfi", "[", "z", "]"]], "\[Proportional]", " ", RowBox[List[RowBox[List["Erfi", "[", SubscriptBox["z", "0"], "]"]], "+", RowBox[List[FractionBox[RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", SubsuperscriptBox["z", "0", "2"]], " "]], SqrtBox["\[Pi]"]], RowBox[List["(", RowBox[List["z", "-", SubscriptBox["z", "0"]]], ")"]]]], "+", RowBox[List[FractionBox[RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", SubsuperscriptBox["z", "0", "2"]], " ", SubscriptBox["z", "0"]]], SqrtBox["\[Pi]"]], SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", SubscriptBox["z", "0"]]], ")"]], "2"]]], "+", RowBox[List["O", "[", SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", SubscriptBox["z", "0"]]], ")"]], "3"], "]"]]]]]]]]








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> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8733; </mo> <mrow> <mrow> <mi> erfi </mi> <mo> &#8289; </mo> <mo> ( </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mfrac> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msup> <mi> &#8519; </mi> <msubsup> <mi> z </mi> <mn> 0 </mn> <mn> 2 </mn> </msubsup> </msup> </mrow> <msqrt> <mi> &#960; </mi> </msqrt> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msup> <mi> &#8519; </mi> <msubsup> <mi> z </mi> <mn> 0 </mn> <mn> 2 </mn> </msubsup> </msup> <mo> &#8290; </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> </mrow> <msqrt> <mi> &#960; </mi> </msqrt> </mfrac> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mi> O </mi> <mo> &#8289; </mo> <mo> ( </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Proportional </ci> <apply> <ci> Erfi </ci> <ci> z </ci> </apply> <apply> <plus /> <apply> <ci> Erfi </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <exponentiale /> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <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 /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <exponentiale /> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> <apply> <power /> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <ci> O </ci> <apply> <power /> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> <cn type='integer'> 3 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Erfi", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Erfi", "[", SubscriptBox["zz", "0"], "]"]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", SubsuperscriptBox["zz", "0", "2"]]]], ")"]], " ", RowBox[List["(", RowBox[List["z", "-", SubscriptBox["zz", "0"]]], ")"]]]], SqrtBox["\[Pi]"]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", SubsuperscriptBox["zz", "0", "2"]], " ", SubscriptBox["zz", "0"]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", SubscriptBox["zz", "0"]]], ")"]], "2"]]], SqrtBox["\[Pi]"]], "+", SuperscriptBox[RowBox[List["O", "[", RowBox[List["z", "-", SubscriptBox["zz", "0"]]], "]"]], "3"]]]]]]]


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





2007-05-02