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InverseErfc




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > InverseErfc[z] > Differentiation > Low-order differentiation





http://functions.wolfram.com/06.31.20.0001.01









  


  








Input Form





D[InverseErfc[z], z] == (-(Sqrt[Pi]/2)) E^InverseErfc[z]^2








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", "z"], RowBox[List["InverseErfc", "[", "z", "]"]]]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox[SqrtBox["\[Pi]"], "2"]]], " ", SuperscriptBox["\[ExponentialE]", SuperscriptBox[RowBox[List["InverseErfc", "[", "z", "]"]], "2"]], " "]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mfrac> <mrow> <mo> &#8706; </mo> <mrow> <msup> <mi> erfc </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> &#8706; </mo> <mi> z </mi> </mrow> </mfrac> <mo> &#10869; </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <msqrt> <mi> &#960; </mi> </msqrt> <mn> 2 </mn> </mfrac> </mrow> <mo> &#8290; </mo> <msup> <mi> &#8519; </mi> <msup> <mrow> <msup> <mi> erfc </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </msup> <mtext> </mtext> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <partialdiff /> <bvar> <ci> z </ci> </bvar> <apply> <ci> InverseErfc </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <exponentiale /> <apply> <power /> <apply> <ci> InverseErfc </ci> <ci> z </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["z_"]]], RowBox[List["InverseErfc", "[", "z_", "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["-", SqrtBox["\[Pi]"]]], ")"]], " ", SuperscriptBox["\[ExponentialE]", SuperscriptBox[RowBox[List["InverseErfc", "[", "z", "]"]], "2"]]]]]]]]


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





2001-10-29