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http://functions.wolfram.com/07.45.04.0013.01
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BranchCuts[WhittakerW[\[Nu], \[Mu], z], z] ==
{{Interval[{-Infinity, 0}], -I}} /;
!Element[\[Nu] - \[Mu] - 1/2, Integers] && \[Nu] - \[Mu] - 1/2 >= 0 &&
Element[\[Nu], Integers]
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["BranchCuts", "[", RowBox[List[RowBox[List["WhittakerW", "[", RowBox[List["\[Nu]", ",", "\[Mu]", ",", "z"]], "]"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List["{", RowBox[List["{", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "\[Infinity]"]], ",", "0"]], "}"]], "]"]], ",", RowBox[List["-", "\[ImaginaryI]"]]]], "}"]], "}"]]]], "/;", RowBox[List[RowBox[List["Not", "[", RowBox[List["Element", "[", RowBox[List[RowBox[List["\[Nu]", "-", "\[Mu]", "-", FractionBox["1", "2"]]], ",", "Integers"]], "]"]], "]"]], "\[And]", RowBox[List[RowBox[List["\[Nu]", "-", "\[Mu]", "-", FractionBox["1", "2"]]], ">=", "0"]], "\[And]", RowBox[List["\[Nu]", "\[Element]", "Integers"]]]]]]]]
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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> <mrow> <msub> <mi> ℬ𝒞 </mi> <mi> z </mi> </msub> <mo> ( </mo> <mrow> <msub> <semantics> <mi> W </mi> <annotation encoding='Mathematica'> TagBox["W", WhittakerW] </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> <mo> { </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> ∞ </mi> </mrow> <mo> , </mo> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> <mo> , </mo> <mrow> <mo> - </mo> <mi> ⅈ </mi> </mrow> </mrow> <mo> } </mo> </mrow> <mo> } </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mrow> <mi> ν </mi> <mo> - </mo> <mi> μ </mi> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ∉ </mo> <semantics> <mi> ℕ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalN]", Function[Integers]] </annotation> </semantics> </mrow> <mo> ∧ </mo> <mrow> <mi> ν </mi> <mo> ∈ </mo> <semantics> <mi> ℤ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalZ]", Function[List[], Integers]] </annotation> </semantics> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <mrow> <msub> <mi> ℬ𝒞 </mi> <mi> z </mi> </msub> <mo> ( </mo> <mrow> <msub> <semantics> <mi> W </mi> <annotation encoding='Mathematica'> TagBox["W", WhittakerW] </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> <mo> { </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> ∞ </mi> </mrow> <mo> , </mo> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> <mo> , </mo> <mrow> <mo> - </mo> <mi> ⅈ </mi> </mrow> </mrow> <mo> } </mo> </mrow> <mo> } </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mrow> <mi> ν </mi> <mo> - </mo> <mi> μ </mi> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ∉ </mo> <semantics> <mi> ℕ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalN]", Function[Integers]] </annotation> </semantics> </mrow> <mo> ∧ </mo> <mrow> <mi> ν </mi> <mo> ∈ </mo> <semantics> <mi> ℤ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalZ]", Function[List[], Integers]] </annotation> </semantics> </mrow> </mrow> </mrow> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["BranchCuts", "[", RowBox[List[RowBox[List["WhittakerW", "[", RowBox[List["\[Nu]_", ",", "\[Mu]_", ",", "z_"]], "]"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["{", RowBox[List["{", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "\[Infinity]"]], ",", "0"]], "}"]], "]"]], ",", RowBox[List["-", "\[ImaginaryI]"]]]], "}"]], "}"]], "/;", RowBox[List[RowBox[List["!", RowBox[List[RowBox[List["\[Nu]", "-", "\[Mu]", "-", FractionBox["1", "2"]]], "\[Element]", "Integers"]]]], "&&", RowBox[List[RowBox[List["\[Nu]", "-", "\[Mu]", "-", FractionBox["1", "2"]]], "\[GreaterEqual]", "0"]], "&&", RowBox[List["\[Nu]", "\[Element]", "Integers"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
