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variants of this functions
HermiteH




Mathematica Notation

Traditional Notation









Polynomials > HermiteH[n,z] > Series representations > Generalized power series > Expansions at generic point z==z0 > For the function itself





http://functions.wolfram.com/05.01.06.0010.01









  


  








Input Form





HermiteH[n, z] == HermiteH[n, Subscript[z, 0]] + 2 n HermiteH[-1 + n, Subscript[z, 0]] (z - Subscript[z, 0]) + (-1 + n) n HermiteH[-2 + n, Subscript[z, 0]] (z - Subscript[z, 0])^2 + O[(z - Subscript[z, 0])^3]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["HermiteH", "[", RowBox[List["n", ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["HermiteH", "[", RowBox[List["n", ",", SubscriptBox["z", "0"]]], "]"]], "+", RowBox[List["2", " ", "n", " ", RowBox[List["HermiteH", "[", RowBox[List[RowBox[List[RowBox[List["-", "1"]], "+", "n"]], ",", SubscriptBox["z", "0"]]], "]"]], " ", RowBox[List["(", RowBox[List["z", "-", SubscriptBox["z", "0"]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "n"]], ")"]], " ", "n", " ", RowBox[List["HermiteH", "[", RowBox[List[RowBox[List[RowBox[List["-", "2"]], "+", "n"]], ",", SubscriptBox["z", "0"]]], "]"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", SubscriptBox["z", "0"]]], ")"]], "2"]]], "+", RowBox[List["O", "[", SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", SubscriptBox["z", "0"]]], ")"]], "3"], "]"]]]]]]]]








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> H </mi> <mi> n </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <msub> <mi> H </mi> <mi> n </mi> </msub> <mo> ( </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> n </mi> <mo> &#8290; </mo> <mrow> <msub> <mi> H </mi> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> <mo> ( </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> n </mi> <mo> &#8290; </mo> <mrow> <msub> <mi> H </mi> <mrow> <mi> n </mi> <mo> - </mo> <mn> 2 </mn> </mrow> </msub> <mo> ( </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mi> O </mi> <mo> &#8289; </mo> <mo> ( </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HermiteH </ci> <ci> n </ci> <ci> z </ci> </apply> <apply> <plus /> <apply> <ci> HermiteH </ci> <ci> n </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> <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> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> <ci> n </ci> <apply> <ci> HermiteH </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> -2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <ci> O </ci> <apply> <power /> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> <cn type='integer'> 3 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HermiteH", "[", RowBox[List["n_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["HermiteH", "[", RowBox[List["n", ",", SubscriptBox["zz", "0"]]], "]"]], "+", RowBox[List["2", " ", "n", " ", RowBox[List["HermiteH", "[", RowBox[List[RowBox[List[RowBox[List["-", "1"]], "+", "n"]], ",", SubscriptBox["zz", "0"]]], "]"]], " ", RowBox[List["(", RowBox[List["z", "-", SubscriptBox["zz", "0"]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "n"]], ")"]], " ", "n", " ", RowBox[List["HermiteH", "[", RowBox[List[RowBox[List[RowBox[List["-", "2"]], "+", "n"]], ",", SubscriptBox["zz", "0"]]], "]"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", SubscriptBox["zz", "0"]]], ")"]], "2"]]], "+", SuperscriptBox[RowBox[List["O", "[", RowBox[List["z", "-", SubscriptBox["zz", "0"]]], "]"]], "3"]]]]]]]


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





2007-05-02