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variants of this functions
LegendreQ




Mathematica Notation

Traditional Notation









Hypergeometric Functions > LegendreQ[nu,mu,2,z] > Primary definition





http://functions.wolfram.com/07.11.02.0002.01









  


  








Input Form





LegendreQ[\[Nu], \[Mu], 2, z] == Limit[LegendreQ[\[Nu], OverTilde[\[Mu]], 2, z], OverTilde[\[Mu]] -> \[Mu]] /; Element[\[Mu], Integers]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["LegendreQ", "[", RowBox[List["\[Nu]", ",", "\[Mu]", ",", "2", ",", "z"]], "]"]], "\[Equal]", RowBox[List["Limit", "[", RowBox[List[RowBox[List["LegendreQ", "[", RowBox[List["\[Nu]", ",", OverscriptBox["\[Mu]", "~"], ",", "2", ",", "z"]], "]"]], ",", RowBox[List[OverscriptBox["\[Mu]", "~"], "\[Rule]", "\[Mu]"]]]], "]"]]]], "/;", RowBox[List["Element", "[", RowBox[List["\[Mu]", ",", "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> <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> &#10869; </mo> <mrow> <munder> <mi> lim </mi> <mrow> <mover> <mi> &#956; </mi> <mo> ~ </mo> </mover> <semantics> <mo> &#8594; </mo> <annotation encoding='Mathematica'> &quot;\[Rule]&quot; </annotation> </semantics> <mi> &#956; </mi> </mrow> </munder> <mo> &#8290; </mo> <mtext> &#8201; </mtext> <mrow> <msubsup> <semantics> <mi> Q </mi> <annotation encoding='Mathematica'> TagBox[&quot;Q&quot;, LegendreQ] </annotation> </semantics> <mi> &#957; </mi> <mover> <mi> &#956; </mi> <mo> ~ </mo> </mover> </msubsup> <mo> ( </mo> <semantics> <mi> z </mi> <annotation encoding='Mathematica'> TagBox[&quot;z&quot;, HoldComplete[LegendreQ, 2]] </annotation> </semantics> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> &#956; </mi> <mo> &#8712; </mo> <semantics> <mi> &#8484; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalZ]&quot;, Function[Integers]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> LegendreQ </ci> <ci> &#957; </ci> <ci> &#956; </ci> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> <apply> <limit /> <bvar> <apply> <ci> OverTilde </ci> <ci> &#956; </ci> </apply> </bvar> <condition> <apply> <tendsto /> <apply> <ci> OverTilde </ci> <ci> &#956; </ci> </apply> <ci> &#956; </ci> </apply> </condition> <apply> <ci> LegendreQ </ci> <ci> &#957; </ci> <apply> <ci> OverTilde </ci> <ci> &#956; </ci> </apply> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> </apply> </apply> <apply> <in /> <ci> &#956; </ci> <integers /> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LegendreQ", "[", RowBox[List["\[Nu]_", ",", "\[Mu]_", ",", "2", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Limit", "[", RowBox[List[RowBox[List["LegendreQ", "[", RowBox[List["\[Nu]", ",", OverscriptBox["\[Mu]", "~"], ",", "2", ",", "z"]], "]"]], ",", RowBox[List[OverscriptBox["\[Mu]", "~"], "\[Rule]", "\[Mu]"]]]], "]"]], "/;", RowBox[List["\[Mu]", "\[Element]", "Integers"]]]]]]]]


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





2001-10-29