Inverse of the generalized error function: Series representations (formula 06.30.06.0003)

InverseErf

$Mathematica Notation$

Gamma, Beta, Erf

InverseErf[z₁,z₂]

Series representations

Generalized power series

Expansions at z₂=0

http://functions.wolfram.com/06.30.06.0003.01

Input Form

InverseErf[Subscript[z, 1], Subscript[z, 2]] \[Proportional] Subscript[z, 1] + (1/2) E^Subscript[z, 1]^2 Sqrt[Pi] Subscript[z, 2] + ((Pi Subscript[z, 1])/4) E^(2 Subscript[z, 1]^2) Subscript[z, 2]^2 + ((Pi^(3/2) (1 + 4 Subscript[z, 1]^2))/24) E^(3 Subscript[z, 1]^2) Subscript[z, 2]^3 + ((Pi^2 Subscript[z, 1] (7 + 12 Subscript[z, 1]^2))/ 96) E^(4 Subscript[z, 1]^2) Subscript[z, 2]^4 + ((Pi^(5/2) (7 + 8 Subscript[z, 1]^2) (1 + 12 Subscript[z, 1]^2))/960) E^(5 Subscript[z, 1]^2) Subscript[z, 2]^5 + ((Pi^3 Subscript[z, 1] (127 + 652 Subscript[z, 1]^2 + 480 Subscript[z, 1]^4))/5760) E^(6 Subscript[z, 1]^2) Subscript[z, 2]^6 + ((Pi^(7/2) (127 + 3480 Subscript[z, 1]^2 + 10224 Subscript[z, 1]^4 + 5760 Subscript[z, 1]^6))/80640) E^(7 Subscript[z, 1]^2) Subscript[z, 2]^7 + ((Pi^4 Subscript[z, 1] (4369 + 44808 Subscript[z, 1]^2 + 88848 Subscript[z, 1]^4 + 40320 Subscript[z, 1]^6))/645120) E^(8 Subscript[z, 1]^2) Subscript[z, 2]^8 + \[Ellipsis] /; (Subscript[z, 2] -> 0)

Standard Form

Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["InverseErf", "[", RowBox[List[SubscriptBox["z", "1"], ",", SubscriptBox["z", "2"]]], "]"]], "\[Proportional]", RowBox[List[SubscriptBox["z", "1"], "+", RowBox[List[FractionBox["1", "2"], SuperscriptBox["\[ExponentialE]", SubsuperscriptBox["z", "1", "2"]], " ", SqrtBox["\[Pi]"], " ", SubscriptBox["z", "2"]]], "+", RowBox[List[FractionBox[RowBox[List["\[Pi]", " ", SubscriptBox["z", "1"]]], "4"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", SubsuperscriptBox["z", "1", "2"]]]], " ", SubsuperscriptBox["z", "2", "2"]]], " ", "+", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["4", " ", SubsuperscriptBox["z", "1", "2"]]]]], ")"]]]], "24"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["3", SubsuperscriptBox["z", "1", "2"]]]], " ", SubsuperscriptBox["z", "2", "3"]]], "+", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["\[Pi]", "2"], " ", SubscriptBox["z", "1"], " ", RowBox[List["(", RowBox[List["7", "+", RowBox[List["12", " ", SubsuperscriptBox["z", "1", "2"]]]]], ")"]]]], "96"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["4", SubsuperscriptBox["z", "1", "2"]]]], " ", SubsuperscriptBox["z", "2", "4"]]], " ", "+", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["\[Pi]", RowBox[List["5", "/", "2"]]], " ", RowBox[List["(", RowBox[List["7", "+", RowBox[List["8", " ", SubsuperscriptBox["z", "1", "2"]]]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["12", " ", SubsuperscriptBox["z", "1", "2"]]]]], ")"]]]], "960"], SuperscriptBox["\[ExponentialE]", RowBox[List["5", SubsuperscriptBox["z", "1", "2"]]]], SubsuperscriptBox["z", "2", "5"]]], "+", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["\[Pi]", "3"], SubscriptBox["z", "1"], " ", RowBox[List["(", RowBox[List["127", "+", RowBox[List["652", " ", SubsuperscriptBox["z", "1", "2"]]], "+", RowBox[List["480", " ", SubsuperscriptBox["z", "1", "4"]]]]], ")"]]]], "5760"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["6", SubsuperscriptBox["z", "1", "2"]]]], SubsuperscriptBox["z", "2", "6"]]], " ", "+", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["\[Pi]", RowBox[List["7", "/", "2"]]], " ", RowBox[List["(", RowBox[List["127", "+", RowBox[List["3480", " ", SubsuperscriptBox["z", "1", "2"]]], "+", RowBox[List["10224", " ", SubsuperscriptBox["z", "1", "4"]]], "+", RowBox[List["5760", " ", SubsuperscriptBox["z", "1", "6"]]]]], ")"]]]], "80640"], SuperscriptBox["\[ExponentialE]", RowBox[List["7", " ", SubsuperscriptBox["z", "1", "2"]]]], " ", SubsuperscriptBox["z", "2", "7"]]], "+", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["\[Pi]", "4"], " ", SubscriptBox["z", "1"], " ", RowBox[List["(", RowBox[List["4369", "+", RowBox[List["44808", " ", SubsuperscriptBox["z", "1", "2"]]], "+", RowBox[List["88848", " ", SubsuperscriptBox["z", "1", "4"]]], "+", RowBox[List["40320", " ", SubsuperscriptBox["z", "1", "6"]]]]], ")"]]]], "645120"], SuperscriptBox["\[ExponentialE]", RowBox[List["8", " ", SubsuperscriptBox["z", "1", "2"]]]], " ", SubsuperscriptBox["z", "2", "8"]]], "+", "\[Ellipsis]"]]]], "/;", RowBox[List["(", RowBox[List[SubscriptBox["z", "2"], "\[Rule]", "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> <msup> <mi> erf </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ∝ </mo> <mrow> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <msubsup> <mi> z </mi> <mn> 1 </mn> <mn> 2 </mn> </msubsup> </msup> <mo> ⁢ </mo> <msqrt> <mi> π </mi> </msqrt> <mo> ⁢ </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mfrac> <mrow> <mi> π </mi> <mo> ⁢ </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> </mrow> <mn> 4 </mn> </mfrac> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msubsup> <mi> z </mi> <mn> 1 </mn> <mn> 2 </mn> </msubsup> </mrow> </msup> <mo> ⁢ </mo> <msubsup> <mi> z </mi> <mn> 2 </mn> <mn> 2 </mn> </msubsup> </mrow> <mtext> </mtext> <mo> + </mo> <mrow> <mfrac> <mrow> <msup> <mi> π </mi> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msubsup> <mi> z </mi> <mn> 1 </mn> <mn> 2 </mn> </msubsup> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 24 </mn> </mfrac> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <msubsup> <mi> z </mi> <mn> 1 </mn> <mn> 2 </mn> </msubsup> </mrow> </msup> <mo> ⁢ </mo> <msubsup> <mi> z </mi> <mn> 2 </mn> <mn> 3 </mn> </msubsup> </mrow> <mo> + </mo> <mrow> <mfrac> <mrow> <msup> <mi> π </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 7 </mn> <mo> + </mo> <mrow> <mn> 12 </mn> <mo> ⁢ </mo> <msubsup> <mi> z </mi> <mn> 1 </mn> <mn> 2 </mn> </msubsup> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 96 </mn> </mfrac> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msubsup> <mi> z </mi> <mn> 1 </mn> <mn> 2 </mn> </msubsup> </mrow> </msup> <mo> ⁢ </mo> <msubsup> <mi> z </mi> <mn> 2 </mn> <mn> 4 </mn> </msubsup> </mrow> <mtext> </mtext> <mo> + </mo> <mrow> <mfrac> <mrow> <msup> <mi> π </mi> <mrow> <mn> 5 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 7 </mn> <mo> + </mo> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <msubsup> <mi> z </mi> <mn> 1 </mn> <mn> 2 </mn> </msubsup> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mrow> <mn> 12 </mn> <mo> ⁢ </mo> <msubsup> <mi> z </mi> <mn> 1 </mn> <mn> 2 </mn> </msubsup> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 960 </mn> </mfrac> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <msubsup> <mi> z </mi> <mn> 1 </mn> <mn> 2 </mn> </msubsup> </mrow> </msup> <mo> ⁢ </mo> <msubsup> <mi> z </mi> <mn> 2 </mn> <mn> 5 </mn> </msubsup> </mrow> <mo> + </mo> <mrow> <mfrac> <mrow> <msup> <mi> π </mi> <mn> 3 </mn> </msup> <mo> ⁢ </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 127 </mn> <mo> + </mo> <mrow> <mn> 652 </mn> <mo> ⁢ </mo> <msubsup> <mi> z </mi> <mn> 1 </mn> <mn> 2 </mn> </msubsup> </mrow> <mo> + </mo> <mrow> <mn> 480 </mn> <mo> ⁢ </mo> <msubsup> <mi> z </mi> <mn> 1 </mn> <mn> 4 </mn> </msubsup> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 5760 </mn> </mfrac> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mn> 6 </mn> <mo> ⁢ </mo> <msubsup> <mi> z </mi> <mn> 1 </mn> <mn> 2 </mn> </msubsup> </mrow> </msup> <mo> ⁢ </mo> <msubsup> <mi> z </mi> <mn> 2 </mn> <mn> 6 </mn> </msubsup> </mrow> <mo> + </mo> <mrow> <mfrac> <mrow> <msup> <mi> π </mi> <mrow> <mn> 7 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 127 </mn> <mo> + </mo> <mrow> <mn> 3480 </mn> <mo> ⁢ </mo> <msubsup> <mi> z </mi> <mn> 1 </mn> <mn> 2 </mn> </msubsup> </mrow> <mo> + </mo> <mrow> <mn> 10224 </mn> <mo> ⁢ </mo> <msubsup> <mi> z </mi> <mn> 1 </mn> <mn> 4 </mn> </msubsup> </mrow> <mo> + </mo> <mrow> <mn> 5760 </mn> <mo> ⁢ </mo> <msubsup> <mi> z </mi> <mn> 1 </mn> <mn> 6 </mn> </msubsup> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 80640 </mn> </mfrac> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mn> 7 </mn> <mo> ⁢ </mo> <msubsup> <mi> z </mi> <mn> 1 </mn> <mn> 2 </mn> </msubsup> </mrow> </msup> <mo> ⁢ </mo> <msubsup> <mi> z </mi> <mn> 2 </mn> <mn> 7 </mn> </msubsup> </mrow> <mo> + </mo> <mrow> <mfrac> <mrow> <msup> <mi> π </mi> <mn> 4 </mn> </msup> <mo> ⁢ </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 4369 </mn> <mo> + </mo> <mrow> <mn> 44808 </mn> <mo> ⁢ </mo> <msubsup> <mi> z </mi> <mn> 1 </mn> <mn> 2 </mn> </msubsup> </mrow> <mo> + </mo> <mrow> <mn> 88848 </mn> <mo> ⁢ </mo> <msubsup> <mi> z </mi> <mn> 1 </mn> <mn> 4 </mn> </msubsup> </mrow> <mo> + </mo> <mrow> <mn> 40320 </mn> <mo> ⁢ </mo> <msubsup> <mi> z </mi> <mn> 1 </mn> <mn> 6 </mn> </msubsup> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 645120 </mn> </mfrac> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <msubsup> <mi> z </mi> <mn> 1 </mn> <mn> 2 </mn> </msubsup> </mrow> </msup> <mo> ⁢ </mo> <msubsup> <mi> z </mi> <mn> 2 </mn> <mn> 8 </mn> </msubsup> </mrow> <mo> + </mo> <mo> … </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <semantics> <mo> → </mo> <annotation encoding='Mathematica'> "\[Rule]" </annotation> </semantics> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <ci> Proportional </ci> <apply> <ci> InverseErf </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <power /> <exponentiale /> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <apply> <times /> <pi /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <apply> <times /> <apply> <power /> <pi /> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <power /> <cn type='integer'> 24 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <apply> <times /> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <cn type='integer'> 7 </cn> <apply> <times /> <cn type='integer'> 12 </cn> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <power /> <cn type='integer'> 96 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <apply> <times /> <apply> <power /> <pi /> <cn type='rational'> 5 <sep /> 2 </cn> </apply> <apply> <plus /> <cn type='integer'> 7 </cn> <apply> <times /> <cn type='integer'> 8 </cn> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> 12 </cn> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <power /> <cn type='integer'> 960 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 5 </cn> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <apply> <times /> <apply> <power /> <pi /> <cn type='integer'> 3 </cn> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <cn type='integer'> 127 </cn> <apply> <times /> <cn type='integer'> 652 </cn> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 480 </cn> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <power /> <cn type='integer'> 5760 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 6 </cn> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <apply> <times /> <apply> <power /> <pi /> <cn type='rational'> 7 <sep /> 2 </cn> </apply> <apply> <plus /> <cn type='integer'> 127 </cn> <apply> <times /> <cn type='integer'> 3480 </cn> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 10224 </cn> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 5760 </cn> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <power /> <cn type='integer'> 80640 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 7 </cn> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <apply> <times /> <apply> <power /> <pi /> <cn type='integer'> 4 </cn> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <cn type='integer'> 4369 </cn> <apply> <times /> <cn type='integer'> 44808 </cn> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 88848 </cn> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 40320 </cn> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <power /> <cn type='integer'> 645120 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 8 </cn> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 8 </cn> </apply> </apply> <ci> … </ci> </apply> </apply> <apply> <ci> Rule </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 0 </cn> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

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

2007-05-02

InverseErf[z]