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http://functions.wolfram.com/07.01.09.0003.01
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HermiteH[\[Nu], z] == 2^\[Nu] Gamma[\[Nu] + 1]
Limit[JacobiP[\[Nu], a, a, z/Sqrt[a]]/a^(\[Nu]/2), a -> Infinity]
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Cell[BoxData[RowBox[List[RowBox[List["HermiteH", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], "\[Equal]", RowBox[List[SuperscriptBox["2", "\[Nu]"], " ", RowBox[List["Gamma", "[", RowBox[List["\[Nu]", "+", "1"]], "]"]], " ", RowBox[List["Limit", "[", RowBox[List[RowBox[List[SuperscriptBox["a", RowBox[List["-", FractionBox["\[Nu]", "2"]]]], " ", RowBox[List["JacobiP", "[", RowBox[List["\[Nu]", ",", "a", ",", "a", ",", FractionBox["z", SqrtBox["a"]]]], "]"]]]], ",", RowBox[List["a", "\[Rule]", "\[Infinity]"]]]], "]"]]]]]]]]
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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> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <msup> <mn> 2 </mn> <mi> ν </mi> </msup> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> ν </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <munder> <mi> lim </mi> <mrow> <mi> a </mi> <semantics> <mo> → </mo> <annotation encoding='Mathematica'> "\[Rule]" </annotation> </semantics> <mi> ∞ </mi> </mrow> </munder> <mo> ⁢ </mo> <mtext>   </mtext> <mrow> <msup> <mi> a </mi> <mrow> <mo> - </mo> <mfrac> <mi> ν </mi> <mn> 2 </mn> </mfrac> </mrow> </msup> <mo> ⁢ </mo> <mrow> <msubsup> <mi> P </mi> <mi> ν </mi> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> </msubsup> <mo> ( </mo> <mfrac> <mi> z </mi> <msqrt> <mi> a </mi> </msqrt> </mfrac> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HermiteH </ci> <ci> ν </ci> <ci> z </ci> </apply> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <ci> ν </ci> </apply> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> ν </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <limit /> <bvar> <ci> a </ci> </bvar> <condition> <apply> <tendsto /> <ci> a </ci> <infinity /> </apply> </condition> <apply> <times /> <apply> <power /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> ν </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <ci> JacobiP </ci> <ci> ν </ci> <ci> a </ci> <ci> a </ci> <apply> <times /> <ci> z </ci> <apply> <power /> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </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]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox["2", "\[Nu]"], " ", RowBox[List["Gamma", "[", RowBox[List["\[Nu]", "+", "1"]], "]"]], " ", RowBox[List["Limit", "[", RowBox[List[RowBox[List[SuperscriptBox["a", RowBox[List["-", FractionBox["\[Nu]", "2"]]]], " ", RowBox[List["JacobiP", "[", RowBox[List["\[Nu]", ",", "a", ",", "a", ",", FractionBox["z", SqrtBox["a"]]]], "]"]]]], ",", RowBox[List["a", "\[Rule]", "\[Infinity]"]]]], "]"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
