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http://functions.wolfram.com/07.44.03.0011.01
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WhittakerM[0, \[Mu], z] == (4^\[Mu] Gamma[1 + \[Mu]] z^(1/2 + \[Mu])
BesselI[\[Mu], -(z/2)])/(-z)^\[Mu]
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Cell[BoxData[RowBox[List[RowBox[List["WhittakerM", "[", RowBox[List["0", ",", "\[Mu]", ",", "z"]], "]"]], "\[Equal]", RowBox[List[SuperscriptBox["4", "\[Mu]"], " ", RowBox[List["Gamma", "[", RowBox[List["1", "+", "\[Mu]"]], "]"]], SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["-", "\[Mu]"]]], " ", SuperscriptBox["z", RowBox[List[FractionBox["1", "2"], "+", "\[Mu]"]]], " ", RowBox[List["BesselI", "[", RowBox[List["\[Mu]", ",", RowBox[List["-", FractionBox["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> <semantics> <mi> M </mi> <annotation encoding='Mathematica'> TagBox["M", WhittakerM] </annotation> </semantics> <mrow> <mn> 0 </mn> <mo> , </mo> <mi> μ </mi> </mrow> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo>  </mo> <mrow> <msup> <mn> 4 </mn> <mi> μ </mi> </msup> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> μ </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mi> μ </mi> </mrow> </msup> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mi> μ </mi> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </msup> <mo> ⁢ </mo> <mrow> <msub> <mi> I </mi> <mi> μ </mi> </msub> <mo> ( </mo> <mrow> <mo> - </mo> <mfrac> <mi> z </mi> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> WhittakerM </ci> <cn type='integer'> 0 </cn> <ci> μ </ci> <ci> z </ci> </apply> <apply> <times /> <apply> <power /> <cn type='integer'> 4 </cn> <ci> μ </ci> </apply> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> μ </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> μ </ci> </apply> </apply> <apply> <power /> <ci> z </ci> <apply> <plus /> <ci> μ </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <ci> BesselI </ci> <ci> μ </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["WhittakerM", "[", RowBox[List["0", ",", "\[Mu]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox["4", "\[Mu]"], " ", RowBox[List["Gamma", "[", RowBox[List["1", "+", "\[Mu]"]], "]"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["-", "\[Mu]"]]], " ", SuperscriptBox["z", RowBox[List[FractionBox["1", "2"], "+", "\[Mu]"]]], " ", RowBox[List["BesselI", "[", RowBox[List["\[Mu]", ",", RowBox[List["-", FractionBox["z", "2"]]]]], "]"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
