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variants of this functions
LegendreQ




Mathematica Notation

Traditional Notation









Hypergeometric Functions > LegendreQ[nu,mu,3,z] > General characteristics > Poles and essential singularities > With respect to mu





http://functions.wolfram.com/07.12.04.0006.01









  


  








Input Form





Singularities[LegendreQ[\[Nu], \[Mu], 3, z], \[Mu]] == {SequenceList[{-\[Nu] - k, 1}, Element[k, Integers] && k > 0], {ComplexInfinity, Infinity}}








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Singularities", "[", RowBox[List[RowBox[List["LegendreQ", "[", RowBox[List["\[Nu]", ",", "\[Mu]", ",", "3", ",", "z"]], "]"]], ",", "\[Mu]"]], "]"]], "\[Equal]", RowBox[List["{", RowBox[List[RowBox[List["SequenceList", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[RowBox[List["-", "\[Nu]"]], "-", "k"]], ",", "1"]], "}"]], ",", RowBox[List[RowBox[List["k", "\[Element]", "Integers"]], "\[And]", RowBox[List["k", ">", "0"]]]]]], "]"]], ",", RowBox[List["{", RowBox[List["ComplexInfinity", ",", "\[Infinity]"]], "}"]]]], "}"]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msub> <mi> &#119982;&#119998;&#120003;&#8458; </mi> <mi> &#956; </mi> </msub> <mo> ( </mo> <semantics> <mrow> <mstyle scriptlevel='0'> <msubsup> <mi> &#120084; </mi> <mi> &#957; </mi> <mi> &#956; </mi> </msubsup> </mstyle> <mo> ( </mo> <mstyle scriptlevel='0'> <mi> z </mi> </mstyle> <mstyle scriptlevel='0'> <mo> ) </mo> </mstyle> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[StyleBox[SubsuperscriptBox[TagBox[&quot;\[GothicCapitalQ]&quot;, LegendreQ], &quot;\[Nu]&quot;, &quot;\[Mu]&quot;], Rule[ScriptLevel, 0]], &quot;(&quot;, StyleBox[&quot;z&quot;, Rule[ScriptLevel, 0]], StyleBox[&quot;)&quot;, Rule[ScriptLevel, 0]]]], Fibonacci] </annotation> </semantics> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mo> { </mo> <mrow> <mrow> <mo> { </mo> <mrow> <mrow> <mo> { </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mi> &#957; </mi> </mrow> <mo> - </mo> <mi> k </mi> </mrow> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> } </mo> </mrow> <mo> /; </mo> <mrow> <mi> k </mi> <mo> &#8712; </mo> <msup> <mi> &#8469; </mi> <mo> + </mo> </msup> </mrow> </mrow> <mo> } </mo> </mrow> <mo> , </mo> <mrow> <mo> { </mo> <mrow> <mover> <mi> &#8734; </mi> <mo> ~ </mo> </mover> <mo> , </mo> <mi> &#8734; </mi> </mrow> <mo> } </mo> </mrow> </mrow> <mo> } </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <msub> <mi> &#119982;&#119998;&#120003;&#8458; </mi> <mi> &#956; </mi> </msub> <mo> ( </mo> <semantics> <mrow> <mstyle scriptlevel='0'> <msubsup> <mi> &#120084; </mi> <mi> &#957; </mi> <mi> &#956; </mi> </msubsup> </mstyle> <mo> ( </mo> <mstyle scriptlevel='0'> <mi> z </mi> </mstyle> <mstyle scriptlevel='0'> <mo> ) </mo> </mstyle> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[StyleBox[SubsuperscriptBox[TagBox[&quot;\[GothicCapitalQ]&quot;, LegendreQ], &quot;\[Nu]&quot;, &quot;\[Mu]&quot;], Rule[ScriptLevel, 0]], &quot;(&quot;, StyleBox[&quot;z&quot;, Rule[ScriptLevel, 0]], StyleBox[&quot;)&quot;, Rule[ScriptLevel, 0]]]], Fibonacci] </annotation> </semantics> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mo> { </mo> <mrow> <mrow> <mo> { </mo> <mrow> <mrow> <mo> { </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mi> &#957; </mi> </mrow> <mo> - </mo> <mi> k </mi> </mrow> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> } </mo> </mrow> <mo> /; </mo> <mrow> <mi> k </mi> <mo> &#8712; </mo> <msup> <mi> &#8469; </mi> <mo> + </mo> </msup> </mrow> </mrow> <mo> } </mo> </mrow> <mo> , </mo> <mrow> <mo> { </mo> <mrow> <mover> <mi> &#8734; </mi> <mo> ~ </mo> </mover> <mo> , </mo> <mi> &#8734; </mi> </mrow> <mo> } </mo> </mrow> </mrow> <mo> } </mo> </mrow> </mrow> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Singularities", "[", RowBox[List[RowBox[List["LegendreQ", "[", RowBox[List["\[Nu]_", ",", "\[Mu]_", ",", "3", ",", "z_"]], "]"]], ",", "\[Mu]_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["{", RowBox[List[RowBox[List["SequenceList", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[RowBox[List["-", "\[Nu]"]], "-", "k"]], ",", "1"]], "}"]], ",", RowBox[List[RowBox[List["k", "\[Element]", "Integers"]], "&&", RowBox[List["k", ">", "0"]]]]]], "]"]], ",", RowBox[List["{", RowBox[List["ComplexInfinity", ",", "\[Infinity]"]], "}"]]]], "}"]]]]]]


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





2001-10-29