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variants of this functions
LegendreP




Mathematica Notation

Traditional Notation









Hypergeometric Functions > LegendreP[nu,mu,3,z] > General characteristics > Branch cuts > With respect to z





http://functions.wolfram.com/07.09.04.0021.01









  


  








Input Form





BranchCuts[LegendreP[\[Nu], \[Mu], 3, z], z] == {{Interval[{-Infinity, -1}], -I}} /; !Element[\[Nu], Integers] && Element[\[Mu]/2, Integers]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["BranchCuts", "[", RowBox[List[RowBox[List["LegendreP", "[", RowBox[List["\[Nu]", ",", "\[Mu]", ",", "3", ",", "z"]], "]"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List["{", RowBox[List["{", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "\[Infinity]"]], ",", RowBox[List["-", "1"]]]], "}"]], "]"]], ",", RowBox[List["-", "\[ImaginaryI]"]]]], "}"]], "}"]]]], "/;", RowBox[List[RowBox[List["Not", "[", RowBox[List["Element", "[", RowBox[List["\[Nu]", ",", "Integers"]], "]"]], "]"]], "\[And]", RowBox[List["Element", "[", RowBox[List[FractionBox["\[Mu]", "2"], ",", "Integers"]], "]"]]]]]]]]








MathML Form







<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> &#8492;&#119966; </mi> <mi> z </mi> </msub> <mo> ( </mo> <mrow> <mstyle scriptlevel='0'> <msubsup> <semantics> <mi> &#120083; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[GothicCapitalP]&quot;, LegendreQ] </annotation> </semantics> <mi> &#957; </mi> <mi> &#956; </mi> </msubsup> </mstyle> <mo> ( </mo> <mstyle scriptlevel='0'> <mi> z </mi> </mstyle> <mstyle scriptlevel='0'> <mo> ) </mo> </mstyle> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mo> { </mo> <mrow> <mo> { </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> &#8734; </mi> </mrow> <mo> , </mo> <mrow> <mo> - </mo> <mi> &#8520; </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> , </mo> <mrow> <mo> - </mo> <mi> &#8520; </mi> </mrow> </mrow> <mo> } </mo> </mrow> <mo> } </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> &#957; </mi> <mo> &#8713; </mo> <mi> &#8484; </mi> </mrow> <mo> &#8743; </mo> <mrow> <mfrac> <mi> &#956; </mi> <mn> 2 </mn> </mfrac> <mo> &#8712; </mo> <mi> &#8484; </mi> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <mrow> <msub> <mi> &#8492;&#119966; </mi> <mi> z </mi> </msub> <mo> ( </mo> <mrow> <mstyle scriptlevel='0'> <msubsup> <semantics> <mi> &#120083; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[GothicCapitalP]&quot;, LegendreQ] </annotation> </semantics> <mi> &#957; </mi> <mi> &#956; </mi> </msubsup> </mstyle> <mo> ( </mo> <mstyle scriptlevel='0'> <mi> z </mi> </mstyle> <mstyle scriptlevel='0'> <mo> ) </mo> </mstyle> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mo> { </mo> <mrow> <mo> { </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> &#8734; </mi> </mrow> <mo> , </mo> <mrow> <mo> - </mo> <mi> &#8520; </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> , </mo> <mrow> <mo> - </mo> <mi> &#8520; </mi> </mrow> </mrow> <mo> } </mo> </mrow> <mo> } </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> &#957; </mi> <mo> &#8713; </mo> <mi> &#8484; </mi> </mrow> <mo> &#8743; </mo> <mrow> <mfrac> <mi> &#956; </mi> <mn> 2 </mn> </mfrac> <mo> &#8712; </mo> <mi> &#8484; </mi> </mrow> </mrow> </mrow> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["BranchCuts", "[", RowBox[List[RowBox[List["LegendreP", "[", RowBox[List["\[Nu]_", ",", "\[Mu]_", ",", "3", ",", "z_"]], "]"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["{", RowBox[List["{", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "\[Infinity]"]], ",", RowBox[List["-", "1"]]]], "}"]], "]"]], ",", RowBox[List["-", "\[ImaginaryI]"]]]], "}"]], "}"]], "/;", RowBox[List[RowBox[List["!", RowBox[List["\[Nu]", "\[Element]", "Integers"]]]], "&&", RowBox[List[FractionBox["\[Mu]", "2"], "\[Element]", "Integers"]]]]]]]]]]


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





2001-10-29