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variants of this functions
LegendreQ




Mathematica Notation

Traditional Notation









Hypergeometric Functions > LegendreQ[nu,mu,2,z] > General characteristics > Branch points > With respect to z





http://functions.wolfram.com/07.11.04.0016.01









  


  








Input Form





RamificationIndex[LegendreQ[\[Nu], \[Mu], 2, z], z, ComplexInfinity] == Log /; Element[2 \[Nu], Integers] || !Element[\[Nu], Rationals]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["RamificationIndex", "[", RowBox[List[RowBox[List["LegendreQ", "[", RowBox[List["\[Nu]", ",", "\[Mu]", ",", "2", ",", "z"]], "]"]], ",", "z", ",", "ComplexInfinity"]], "]"]], "\[Equal]", "Log"]], "/;", RowBox[List[RowBox[List["Element", "[", RowBox[List[RowBox[List["2", "\[Nu]"]], ",", "Integers"]], "]"]], "\[Or]", RowBox[List["Not", "[", RowBox[List["Element", "[", RowBox[List["\[Nu]", ",", "Rationals"]], "]"]], "]"]]]]]]]]








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> &#8475; </mi> <mi> z </mi> </msub> <mo> ( </mo> <mrow> <mrow> <msubsup> <semantics> <mi> Q </mi> <annotation encoding='Mathematica'> TagBox[&quot;Q&quot;, LegendreQ] </annotation> </semantics> <mi> &#957; </mi> <mi> &#956; </mi> </msubsup> <mo> ( </mo> <semantics> <mi> z </mi> <annotation encoding='Mathematica'> TagBox[&quot;z&quot;, HoldComplete[LegendreQ, 2]] </annotation> </semantics> <mo> ) </mo> </mrow> <mo> , </mo> <mover> <mi> &#8734; </mi> <mo> ~ </mo> </mover> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mi> log </mi> </mrow> <mo> /; </mo> <mrow> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> <mo> &#8712; </mo> <semantics> <mi> &#8484; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalZ]&quot;, Function[Integers]] </annotation> </semantics> </mrow> <mo> &#8744; </mo> <mrow> <mi> a </mi> <mo> &#8713; </mo> <semantics> <mi> &#8474; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalQ]&quot;, Function[Rationals]] </annotation> </semantics> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <apply> <ci> Subscript </ci> <ci> &#8475; </ci> <ci> z </ci> </apply> <apply> <ci> LegendreQ </ci> <ci> &#957; </ci> <ci> &#956; </ci> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> <apply> <ci> OverTilde </ci> <infinity /> </apply> </apply> <ci> log </ci> </apply> <apply> <or /> <apply> <in /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#957; </ci> </apply> <integers /> </apply> <apply> <notin /> <ci> a </ci> <rationals /> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["RamificationIndex", "[", RowBox[List[RowBox[List["LegendreQ", "[", RowBox[List["\[Nu]_", ",", "\[Mu]_", ",", "2", ",", "z_"]], "]"]], ",", "z_", ",", "ComplexInfinity"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["Log", "/;", RowBox[List[RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "\[Element]", "Integers"]], "||", RowBox[List["!", RowBox[List["\[Nu]", "\[Element]", "Rationals"]]]]]]]]]]]]


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





2001-10-29