|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
http://functions.wolfram.com/05.01.17.0003.01
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
HermiteH[n + 1, z] + 2 n HermiteH[n - 1, z] == 2 z HermiteH[n, z]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["HermiteH", "[", RowBox[List[RowBox[List["n", "+", "1"]], ",", "z"]], "]"]], "+", RowBox[List["2", " ", "n", " ", RowBox[List["HermiteH", "[", RowBox[List[RowBox[List["n", "-", "1"]], ",", "z"]], "]"]]]]]], "\[Equal]", RowBox[List["2", " ", "z", " ", RowBox[List["HermiteH", "[", RowBox[List["n", ",", "z"]], "]"]]]]]]]]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> n </mi> <mo> ⁢ </mo> <mrow> <msub> <mi> H </mi> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <msub> <mi> H </mi> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ⩵ </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <msub> <mi> H </mi> <mi> n </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> n </ci> <apply> <ci> HermiteH </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <ci> HermiteH </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <ci> HermiteH </ci> <ci> n </ci> <ci> z </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
|
|
|
|
|
|
|
|
|
|
| |
|
|
|
|
| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["HermiteH", "[", RowBox[List[RowBox[List["n_", "+", "1"]], ",", "z_"]], "]"]], "+", RowBox[List["2", " ", "n_", " ", RowBox[List["HermiteH", "[", RowBox[List[RowBox[List["n_", "-", "1"]], ",", "z_"]], "]"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List["2", " ", "z", " ", RowBox[List["HermiteH", "[", RowBox[List["n", ",", "z"]], "]"]]]]]]]] |
|
|
|
|
|
|
|
|
|
|
Date Added to functions.wolfram.com (modification date)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|