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http://functions.wolfram.com/07.01.16.0011.01
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HermiteH[\[Nu], -z] == HermiteH[\[Nu], z] -
2^(1 + \[Nu]) z Gamma[(1 + \[Nu])/2] Sin[(Pi \[Nu])/2]
LaguerreL[(\[Nu] - 1)/2, 1/2, z^2]
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Cell[BoxData[RowBox[List[RowBox[List["HermiteH", "[", RowBox[List["\[Nu]", ",", RowBox[List["-", "z"]]]], "]"]], "\[Equal]", RowBox[List[RowBox[List["HermiteH", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], "-", RowBox[List[SuperscriptBox["2", RowBox[List["1", "+", "\[Nu]"]]], " ", "z", " ", RowBox[List["Gamma", "[", FractionBox[RowBox[List["1", "+", "\[Nu]"]], "2"], "]"]], " ", RowBox[List["Sin", "[", FractionBox[RowBox[List["\[Pi]", " ", "\[Nu]"]], "2"], "]"]], RowBox[List["LaguerreL", "[", RowBox[List[FractionBox[RowBox[List["\[Nu]", "-", "1"]], "2"], ",", FractionBox["1", "2"], ",", SuperscriptBox["z", "2"]]], "]"]]]]]]]]]]
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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> H </mi> <mi> ν </mi> </msub> <mo> ( </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo>  </mo> <mrow> <mrow> <msub> <mi> H </mi> <mi> ν </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <msup> <mn> 2 </mn> <mrow> <mi> ν </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msup> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mrow> <mi> ν </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mi> ν </mi> </mrow> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msubsup> <mi> L </mi> <mfrac> <mrow> <mi> ν </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </msubsup> <mo> ( </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HermiteH </ci> <ci> ν </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <ci> HermiteH </ci> <ci> ν </ci> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> ν </ci> <cn type='integer'> 1 </cn> </apply> </apply> <ci> z </ci> <apply> <ci> Gamma </ci> <apply> <times /> <apply> <plus /> <ci> ν </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <sin /> <apply> <times /> <pi /> <ci> ν </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ci> LaguerreL </ci> <apply> <times /> <apply> <plus /> <ci> ν </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HermiteH", "[", RowBox[List["\[Nu]_", ",", RowBox[List["-", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["HermiteH", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], "-", RowBox[List[SuperscriptBox["2", RowBox[List["1", "+", "\[Nu]"]]], " ", "z", " ", RowBox[List["Gamma", "[", FractionBox[RowBox[List["1", "+", "\[Nu]"]], "2"], "]"]], " ", RowBox[List["Sin", "[", FractionBox[RowBox[List["\[Pi]", " ", "\[Nu]"]], "2"], "]"]], " ", RowBox[List["LaguerreL", "[", RowBox[List[FractionBox[RowBox[List["\[Nu]", "-", "1"]], "2"], ",", FractionBox["1", "2"], ",", SuperscriptBox["z", "2"]]], "]"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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