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http://functions.wolfram.com/07.44.04.0004.01
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Singularities[WhittakerM[\[Nu], \[Mu], z], \[Mu]] ==
{SequenceList[{-((k + 1)/2), 1}, Element[k, Integers] && k >= 0],
{ComplexInfinity, Infinity}}
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Cell[BoxData[RowBox[List[RowBox[List["Singularities", "[", RowBox[List[RowBox[List["WhittakerM", "[", RowBox[List["\[Nu]", ",", "\[Mu]", ",", "z"]], "]"]], ",", "\[Mu]"]], "]"]], "\[Equal]", RowBox[List["{", RowBox[List[RowBox[List["SequenceList", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FormBox[FractionBox[RowBox[List["k", "+", "1"]], "2"], TraditionalForm]]], ",", "1"]], "}"]], ",", RowBox[List[RowBox[List["k", "\[Element]", "Integers"]], "\[And]", RowBox[List["k", "\[GreaterEqual]", "0"]]]]]], "]"]], ",", RowBox[List["{", RowBox[List["ComplexInfinity", ",", "\[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> 𝒮𝒾𝓃ℊ </mi> <mi> μ </mi> </msub> <mo> ( </mo> <mrow> <msub> <semantics> <mi> M </mi> <annotation encoding='Mathematica'> TagBox["M", WhittakerM] </annotation> </semantics> <mrow> <mi> ν </mi> <mo> , </mo> <mi> μ </mi> </mrow> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mo> { </mo> <mrow> <mrow> <mo> { </mo> <mrow> <mrow> <mo> { </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> k </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> } </mo> </mrow> <mo> /; </mo> <mrow> <mi> k </mi> <mo> ∈ </mo> <mi> ℕ </mi> </mrow> </mrow> <mo> } </mo> </mrow> <mo> , </mo> <mrow> <mo> { </mo> <mrow> <mover> <mi> ∞ </mi> <mo> ~ </mo> </mover> <mo> , </mo> <mi> ∞ </mi> </mrow> <mo> } </mo> </mrow> </mrow> <mo> } </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <apply> <ci> Subscript </ci> <ci> 𝒮𝒾𝓃ℊ </ci> <ci> μ </ci> </apply> <apply> <ci> WhittakerM </ci> <ci> ν </ci> <ci> μ </ci> <ci> z </ci> </apply> </apply> <list> <list> <apply> <ci> Condition </ci> <list> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <ci> k </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> 1 </cn> </list> <apply> <in /> <ci> k </ci> <ci> ℕ </ci> </apply> </apply> </list> <list> <apply> <ci> OverTilde </ci> <infinity /> </apply> <infinity /> </list> </list> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Singularities", "[", RowBox[List[RowBox[List["WhittakerM", "[", RowBox[List["\[Nu]_", ",", "\[Mu]_", ",", "z_"]], "]"]], ",", "\[Mu]_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["{", RowBox[List[RowBox[List["SequenceList", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", RowBox[List["(", RowBox[List["k", "+", "1"]], ")"]]]], ",", "1"]], "}"]], ",", RowBox[List[RowBox[List["k", "\[Element]", "Integers"]], "&&", RowBox[List["k", "\[GreaterEqual]", "0"]]]]]], "]"]], ",", RowBox[List["{", RowBox[List["ComplexInfinity", ",", "\[Infinity]"]], "}"]]]], "}"]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
