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WhittakerM




Mathematica Notation

Traditional Notation









Hypergeometric Functions > WhittakerM[nu,mu,z] > Operations > Limit operation





http://functions.wolfram.com/07.44.25.0002.01









  


  








Input Form





Limit[(-(z/\[Nu]))^(-(1/2) - \[Mu]) WhittakerM[\[Nu], \[Mu], -(z/\[Nu])], \[Nu] -> Infinity] == (BesselI[2 \[Mu], 2 Sqrt[z]] Gamma[1 + 2 \[Mu]])/ z^\[Mu]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Limit", "[", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox["z", "\[Nu]"]]], ")"]], RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "-", "\[Mu]"]]], " ", RowBox[List["WhittakerM", "[", RowBox[List["\[Nu]", ",", "\[Mu]", ",", RowBox[List["-", FractionBox["z", "\[Nu]"]]]]], "]"]]]], ",", RowBox[List["\[Nu]", "\[Rule]", "\[Infinity]"]]]], "]"]], "\[Equal]", RowBox[List[SuperscriptBox["z", RowBox[List["-", "\[Mu]"]]], " ", RowBox[List["BesselI", "[", RowBox[List[RowBox[List["2", " ", "\[Mu]"]], ",", RowBox[List["2", " ", SqrtBox["z"]]]]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["1", "+", RowBox[List["2", " ", "\[Mu]"]]]], "]"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <munder> <mi> lim </mi> <mrow> <mi> &#957; </mi> <semantics> <mo> &#8594; </mo> <annotation encoding='Mathematica'> &quot;\[Rule]&quot; </annotation> </semantics> <mi> &#8734; </mi> </mrow> </munder> <mo> &#8290; </mo> <mtext> &#8201; </mtext> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mfrac> <mi> z </mi> <mi> &#957; </mi> </mfrac> </mrow> <mo> ) </mo> </mrow> <mrow> <mrow> <mo> - </mo> <mi> &#956; </mi> </mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </msup> <mo> &#8290; </mo> <mrow> <msub> <semantics> <mi> M </mi> <annotation encoding='Mathematica'> TagBox[&quot;M&quot;, WhittakerM] </annotation> </semantics> <mrow> <mi> &#957; </mi> <mo> , </mo> <mi> &#956; </mi> </mrow> </msub> <mo> ( </mo> <mrow> <mo> - </mo> <mfrac> <mi> z </mi> <mi> &#957; </mi> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> &#63449; </mo> <mrow> <msup> <mi> z </mi> <mrow> <mo> - </mo> <mi> &#956; </mi> </mrow> </msup> <mo> &#8290; </mo> <mrow> <msub> <mi> I </mi> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#956; </mi> </mrow> </msub> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#956; </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <limit /> <bvar> <ci> &#957; </ci> </bvar> <condition> <apply> <tendsto /> <ci> &#957; </ci> <infinity /> </apply> </condition> <apply> <times /> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> z </ci> <apply> <power /> <ci> &#957; </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#956; </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <ci> WhittakerM </ci> <ci> &#957; </ci> <ci> &#956; </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> z </ci> <apply> <power /> <ci> &#957; </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#956; </ci> </apply> </apply> <apply> <ci> BesselI </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#956; </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#956; </ci> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Limit", "[", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox["z_", "\[Nu]_"]]], ")"]], RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "-", "\[Mu]_"]]], " ", RowBox[List["WhittakerM", "[", RowBox[List["\[Nu]_", ",", "\[Mu]_", ",", RowBox[List["-", FractionBox["z_", "\[Nu]_"]]]]], "]"]]]], ",", RowBox[List["\[Nu]_", "\[Rule]", "\[Infinity]"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox["z", RowBox[List["-", "\[Mu]"]]], " ", RowBox[List["BesselI", "[", RowBox[List[RowBox[List["2", " ", "\[Mu]"]], ",", RowBox[List["2", " ", SqrtBox["z"]]]]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["1", "+", RowBox[List["2", " ", "\[Mu]"]]]], "]"]]]]]]]]


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





2007-05-02