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variants of this functions
HermiteH




Mathematica Notation

Traditional Notation









Hypergeometric Functions > HermiteH[nu,z] > Differential equations > Ordinary linear differential equations and wronskians





http://functions.wolfram.com/07.01.13.0006.01









  


  








Input Form





Wronskian[HermiteH[\[Nu], z], E^z^2 HermiteH[-1 - \[Nu], I z], z] == (-I) E^(z^2 - (I Pi \[Nu])/2)








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Wronskian", "[", RowBox[List[RowBox[List["HermiteH", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], ",", RowBox[List[SuperscriptBox["\[ExponentialE]", SuperscriptBox["z", "2"]], RowBox[List["HermiteH", "[", RowBox[List[RowBox[List[RowBox[List["-", "1"]], "-", "\[Nu]"]], ",", RowBox[List["\[ImaginaryI]", " ", "z"]]]], "]"]]]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[SuperscriptBox["z", "2"], "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]", " ", "\[Nu]"]], "2"]]]]]]]]]]








MathML Form







<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> <msub> <mi> H </mi> <mi> &#957; </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> , </mo> <mrow> <msup> <mi> &#8519; </mi> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </msup> <mo> &#8290; </mo> <mrow> <msub> <mi> H </mi> <mrow> <mrow> <mo> - </mo> <mi> &#957; </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> <mo> ( </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mo> - </mo> <mi> &#8520; </mi> </mrow> <mo> &#8290; </mo> <msup> <mi> &#8519; </mi> <mrow> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mfrac> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> &#960; </mi> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> <mn> 2 </mn> </mfrac> </mrow> </msup> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <apply> <ci> Subscript </ci> <ci> W </ci> <ci> z </ci> </apply> <apply> <ci> HermiteH </ci> <ci> &#957; </ci> <ci> z </ci> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <ci> HermiteH </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <times /> <imaginaryi /> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <apply> <power /> <exponentiale /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <pi /> <ci> &#957; </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Wronskian", "[", RowBox[List[RowBox[List["HermiteH", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], ",", RowBox[List[SuperscriptBox["\[ExponentialE]", SuperscriptBox["z_", "2"]], " ", RowBox[List["HermiteH", "[", RowBox[List[RowBox[List[RowBox[List["-", "1"]], "-", "\[Nu]_"]], ",", RowBox[List["\[ImaginaryI]", " ", "z_"]]]], "]"]]]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[SuperscriptBox["z", "2"], "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]", " ", "\[Nu]"]], "2"]]]]]]]]]]


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





2007-05-02