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http://functions.wolfram.com/06.25.13.0005.01
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Wronskian[Erf[g[z]], 1, z] == -((2 Derivative[1][g][z])/(E^g[z]^2 Sqrt[Pi]))
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Cell[BoxData[RowBox[List[RowBox[List["Wronskian", "[", RowBox[List[RowBox[List["Erf", "[", RowBox[List["g", "[", "z", "]"]], "]"]], ",", "1", ",", "z"]], "]"]], "\[Equal]", RowBox[List["-", FractionBox[RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", SuperscriptBox[RowBox[List["g", "[", "z", "]"]], "2"]]]], RowBox[List[SuperscriptBox["g", "\[Prime]", Rule[MultilineFunction, None]], "[", "z", "]"]]]], SqrtBox["\[Pi]"]]]]]]]]
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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> <msub> <mi> W </mi> <mi> z </mi> </msub> <mo> ( </mo> <mrow> <mrow> <mi> erf </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> g </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mo> - </mo> <msup> <mrow> <mi> g </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> </msup> <mo> ⁢ </mo> <mrow> <msup> <mi> g </mi> <mo> ′ </mo> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <msqrt> <mi> π </mi> </msqrt> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <apply> <ci> Subscript </ci> <ci> W </ci> <ci> z </ci> </apply> <apply> <ci> Erf </ci> <apply> <ci> g </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <ci> g </ci> <ci> z </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <partialdiff /> <bvar> <ci> z </ci> </bvar> <apply> <ci> g </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Wronskian", "[", RowBox[List[RowBox[List["Erf", "[", RowBox[List["g", "[", "z_", "]"]], "]"]], ",", "1", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", SuperscriptBox[RowBox[List["g", "[", "z", "]"]], "2"]]]], " ", RowBox[List[SuperscriptBox["g", "\[Prime]", Rule[MultilineFunction, None]], "[", "z", "]"]]]], SqrtBox["\[Pi]"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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