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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 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





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MathML Form







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</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> 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<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> &#8230; </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





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["InverseErf", "[", RowBox[List[SubscriptBox["z_", "1"], ",", SubscriptBox["z_", "2"]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SubscriptBox["zz", "1"], "+", RowBox[List[FractionBox["1", "2"], " ", SuperscriptBox["\[ExponentialE]", SubsuperscriptBox["zz", "1", "2"]], " ", SqrtBox["\[Pi]"], " ", SubscriptBox["zz", "2"]]], "+", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["\[Pi]", " ", SubscriptBox["zz", "1"]]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", SubsuperscriptBox["zz", "1", "2"]]]], " ", SubsuperscriptBox["zz", "2", "2"]]], "+", RowBox[List[FractionBox["1", "24"], " ", RowBox[List["(", RowBox[List[SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["4", " ", SubsuperscriptBox["zz", "1", "2"]]]]], ")"]]]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["3", " ", SubsuperscriptBox["zz", "1", "2"]]]], " ", SubsuperscriptBox["zz", "2", "3"]]], "+", RowBox[List[FractionBox["1", "96"], " ", RowBox[List["(", RowBox[List[SuperscriptBox["\[Pi]", "2"], " ", SubscriptBox["zz", "1"], " ", RowBox[List["(", RowBox[List["7", "+", RowBox[List["12", " ", SubsuperscriptBox["zz", "1", "2"]]]]], ")"]]]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["4", " ", SubsuperscriptBox["zz", "1", "2"]]]], " ", SubsuperscriptBox["zz", "2", "4"]]], "+", RowBox[List[FractionBox["1", "960"], " ", RowBox[List["(", RowBox[List[SuperscriptBox["\[Pi]", RowBox[List["5", "/", "2"]]], " ", RowBox[List["(", RowBox[List["7", "+", RowBox[List["8", " ", SubsuperscriptBox["zz", "1", "2"]]]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["12", " ", SubsuperscriptBox["zz", "1", "2"]]]]], ")"]]]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["5", " ", SubsuperscriptBox["zz", "1", "2"]]]], " ", SubsuperscriptBox["zz", "2", "5"]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["\[Pi]", "3"], " ", SubscriptBox["zz", "1"], " ", RowBox[List["(", RowBox[List["127", "+", RowBox[List["652", " ", SubsuperscriptBox["zz", "1", "2"]]], "+", RowBox[List["480", " ", SubsuperscriptBox["zz", "1", "4"]]]]], ")"]]]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["6", " ", SubsuperscriptBox["zz", "1", "2"]]]], " ", SubsuperscriptBox["zz", "2", "6"]]], "5760"], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["\[Pi]", RowBox[List["7", "/", "2"]]], " ", RowBox[List["(", RowBox[List["127", "+", RowBox[List["3480", " ", SubsuperscriptBox["zz", "1", "2"]]], "+", RowBox[List["10224", " ", SubsuperscriptBox["zz", "1", "4"]]], "+", RowBox[List["5760", " ", SubsuperscriptBox["zz", "1", "6"]]]]], ")"]]]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["7", " ", SubsuperscriptBox["zz", "1", "2"]]]], " ", SubsuperscriptBox["zz", "2", "7"]]], "80640"], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["\[Pi]", "4"], " ", SubscriptBox["zz", "1"], " ", RowBox[List["(", RowBox[List["4369", "+", RowBox[List["44808", " ", SubsuperscriptBox["zz", "1", "2"]]], "+", RowBox[List["88848", " ", SubsuperscriptBox["zz", "1", "4"]]], "+", RowBox[List["40320", " ", SubsuperscriptBox["zz", "1", "6"]]]]], ")"]]]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["8", " ", SubsuperscriptBox["zz", "1", "2"]]]], " ", SubsuperscriptBox["zz", "2", "8"]]], "645120"], "+", "\[Ellipsis]"]], "/;", RowBox[List["(", RowBox[List[SubscriptBox["zz", "2"], "\[Rule]", "0"]], ")"]]]]]]]]










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





2007-05-02





© 1998- Wolfram Research, Inc.