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http://functions.wolfram.com/06.29.20.0004.01
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D[InverseErf[z], {z, 4}] == (1/4) E^(4 w^2) Pi^2 w (7 + 12 w^2) /;
w == InverseErf[z]
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["{", RowBox[List["z", ",", "4"]], "}"]]], RowBox[List["InverseErf", "[", "z", "]"]]]], "\[Equal]", RowBox[List[FractionBox["1", "4"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["4", " ", SuperscriptBox["w", "2"]]]], " ", SuperscriptBox["\[Pi]", "2"], " ", "w", " ", RowBox[List["(", RowBox[List["7", "+", RowBox[List["12", " ", SuperscriptBox["w", "2"]]]]], ")"]]]]]], "/;", RowBox[List["w", "\[Equal]", RowBox[List["InverseErf", "[", "z", "]"]]]]]]]]
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mfrac> <mrow> <msup> <mo> ∂ </mo> <mn> 4 </mn> </msup> <mrow> <msup> <mi> erf </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> ∂ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> </mfrac> <mo>  </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msup> <mi> w </mi> <mn> 2 </mn> </msup> </mrow> </msup> <mo> ⁢ </mo> <msup> <mi> π </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <mi> w </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 12 </mn> <mo> ⁢ </mo> <msup> <mi> w </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 7 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> w </mi> <mo>  </mo> <mrow> <msup> <mi> erf </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <partialdiff /> <bvar> <ci> z </ci> <degree> <cn type='integer'> 4 </cn> </degree> </bvar> <apply> <ci> InverseErf </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 4 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> w </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <ci> w </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 12 </cn> <apply> <power /> <ci> w </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 7 </cn> </apply> </apply> </apply> <apply> <eq /> <ci> w </ci> <apply> <ci> InverseErf </ci> <ci> z </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[RowBox[List["{", RowBox[List["z_", ",", "4"]], "}"]]]]], RowBox[List["InverseErf", "[", "z_", "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["1", "4"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["4", " ", SuperscriptBox["w", "2"]]]], " ", SuperscriptBox["\[Pi]", "2"], " ", "w", " ", RowBox[List["(", RowBox[List["7", "+", RowBox[List["12", " ", SuperscriptBox["w", "2"]]]]], ")"]]]], "/;", RowBox[List["w", "\[Equal]", RowBox[List["InverseErf", "[", "z", "]"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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