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variants of this functions
InverseErf




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > InverseErf[z1,z2] > Series representations > Generalized power series > Expansions at z1=0





http://functions.wolfram.com/06.30.06.0001.01









  


  








Input Form





InverseErf[Subscript[z, 1], Subscript[z, 2]] \[Proportional] InverseErf[Subscript[z, 2]] + E^InverseErf[Subscript[z, 2]]^2 (Subscript[z, 1] + InverseErf[Subscript[z, 2]] E^InverseErf[Subscript[z, 2]]^2 Subscript[z, 1]^2 + (-1 + E^(2 InverseErf[Subscript[z, 2]]^2) + 4 E^(2 InverseErf[Subscript[z, 2]]^2) InverseErf[Subscript[z, 2]]^2) (Subscript[z, 1]^3/3) + InverseErf[Subscript[z, 2]] E^InverseErf[Subscript[z, 2]]^2 (-4 + 7 E^(2 InverseErf[Subscript[z, 2]]^2) + 12 E^(2 InverseErf[Subscript[z, 2]]^2) InverseErf[Subscript[z, 2]]^2) (Subscript[z, 1]^4/6) + (3 - 10 E^(2 InverseErf[Subscript[z, 2]]^2) + 7 E^(4 InverseErf[Subscript[z, 2]]^2) - 40 E^(2 InverseErf[Subscript[z, 2]]^2) InverseErf[Subscript[z, 2]]^2 + 92 E^(4 InverseErf[Subscript[z, 2]]^2) InverseErf[Subscript[z, 2]]^2 + 96 E^(4 InverseErf[Subscript[z, 2]]^2) InverseErf[Subscript[z, 2]]^4) (Subscript[z, 1]^5/30) + \[Ellipsis]) /; (Subscript[z, 1] -> 0)








Standard Form





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MathML Form







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</mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> </msup> </mrow> <mo> + </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mfrac> <mrow> <msubsup> <mi> z </mi> <mn> 1 </mn> <mn> 5 </mn> </msubsup> <mtext> </mtext> </mrow> <mn> 30 </mn> </mfrac> </mrow> <mo> + </mo> <mo> &#8230; </mo> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <semantics> <mo> &#8594; </mo> <annotation encoding='Mathematica'> &quot;\[Rule]&quot; </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> InverseErf </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <power /> <apply> <ci> InverseErf </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <power /> <apply> <ci> InverseErf </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <ci> InverseErf </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <ci> InverseErf </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <ci> InverseErf </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <ci> InverseErf </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <times /> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <cn 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<power /> <apply> <ci> InverseErf </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 10 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <ci> InverseErf </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 7 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <apply> <ci> InverseErf </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <times /> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 5 </cn> </apply> <apply> <power /> <cn type='integer'> 30 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <ci> &#8230; </ci> </apply> </apply> </apply> </apply> <apply> <ci> Rule </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 0 </cn> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["InverseErf", "[", RowBox[List[SubscriptBox["z_", "1"], ",", SubscriptBox["z_", "2"]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["InverseErf", "[", SubscriptBox["zz", "2"], "]"]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", SuperscriptBox[RowBox[List["InverseErf", "[", SubscriptBox["zz", "2"], "]"]], "2"]], " ", RowBox[List["(", RowBox[List[SubscriptBox["zz", "1"], "+", RowBox[List[RowBox[List["InverseErf", "[", SubscriptBox["zz", "2"], "]"]], " ", SuperscriptBox["\[ExponentialE]", SuperscriptBox[RowBox[List["InverseErf", "[", SubscriptBox["zz", "2"], "]"]], "2"]], " ", SubsuperscriptBox["zz", "1", "2"]]], "+", RowBox[List[FractionBox["1", "3"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", SuperscriptBox[RowBox[List["InverseErf", "[", SubscriptBox["zz", "2"], "]"]], "2"]]]], "+", RowBox[List["4", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", SuperscriptBox[RowBox[List["InverseErf", "[", SubscriptBox["zz", "2"], "]"]], "2"]]]], " ", SuperscriptBox[RowBox[List["InverseErf", "[", SubscriptBox["zz", "2"], "]"]], "2"]]]]], ")"]], " ", SubsuperscriptBox["zz", "1", "3"]]], "+", RowBox[List[FractionBox["1", "6"], " ", RowBox[List["InverseErf", "[", SubscriptBox["zz", "2"], "]"]], " ", SuperscriptBox["\[ExponentialE]", SuperscriptBox[RowBox[List["InverseErf", "[", SubscriptBox["zz", "2"], "]"]], "2"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "4"]], "+", RowBox[List["7", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", SuperscriptBox[RowBox[List["InverseErf", "[", SubscriptBox["zz", "2"], "]"]], "2"]]]]]], "+", RowBox[List["12", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", SuperscriptBox[RowBox[List["InverseErf", "[", SubscriptBox["zz", "2"], "]"]], "2"]]]], " ", SuperscriptBox[RowBox[List["InverseErf", "[", SubscriptBox["zz", "2"], "]"]], "2"]]]]], ")"]], " ", SubsuperscriptBox["zz", "1", "4"]]], "+", RowBox[List[FractionBox["1", "30"], " ", RowBox[List["(", RowBox[List["3", "-", RowBox[List["10", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", SuperscriptBox[RowBox[List["InverseErf", "[", SubscriptBox["zz", "2"], "]"]], "2"]]]]]], "+", RowBox[List["7", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["4", " ", SuperscriptBox[RowBox[List["InverseErf", "[", SubscriptBox["zz", "2"], "]"]], "2"]]]]]], "-", RowBox[List["40", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", SuperscriptBox[RowBox[List["InverseErf", "[", SubscriptBox["zz", "2"], "]"]], "2"]]]], " ", SuperscriptBox[RowBox[List["InverseErf", "[", SubscriptBox["zz", "2"], "]"]], "2"]]], "+", RowBox[List["92", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["4", " ", SuperscriptBox[RowBox[List["InverseErf", "[", SubscriptBox["zz", "2"], "]"]], "2"]]]], " ", SuperscriptBox[RowBox[List["InverseErf", "[", SubscriptBox["zz", "2"], "]"]], "2"]]], "+", RowBox[List["96", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["4", " ", SuperscriptBox[RowBox[List["InverseErf", "[", SubscriptBox["zz", "2"], "]"]], "2"]]]], " ", SuperscriptBox[RowBox[List["InverseErf", "[", SubscriptBox["zz", "2"], "]"]], "4"]]]]], ")"]], " ", SubsuperscriptBox["zz", "1", "5"]]], "+", "\[Ellipsis]"]], ")"]]]]]], "/;", RowBox[List["(", RowBox[List[SubscriptBox["zz", "1"], "\[Rule]", "0"]], ")"]]]]]]]]


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





2007-05-02