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variants of this functions
LegendreP




Mathematica Notation

Traditional Notation









Hypergeometric Functions > LegendreP[nu,mu,3,z] > Specific values > Specialized values > For fixed nu, mu





http://functions.wolfram.com/07.09.03.0002.01









  


  








Input Form





LegendreP[\[Nu], \[Mu], 3, 1] == 0 /; Re[\[Mu]] < 0 || (Element[\[Mu], Integers] && \[Mu] > 0)








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["LegendreP", "[", RowBox[List["\[Nu]", ",", "\[Mu]", ",", "3", ",", "1"]], "]"]], "\[Equal]", "0"]], "/;", RowBox[List[RowBox[List[RowBox[List["Re", "[", "\[Mu]", "]"]], "<", "0"]], "\[Or]", RowBox[List["(", RowBox[List[RowBox[List["\[Mu]", "\[Element]", "Integers"]], "\[And]", RowBox[List["\[Mu]", ">", "0"]]]], ")"]]]]]]]]








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> <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> <mn> 1 </mn> <mstyle scriptlevel='0'> <mo> ) </mo> </mstyle> </mrow> <mo> &#10869; </mo> <mn> 0 </mn> </mrow> <mo> /; </mo> <mrow> <mrow> <mrow> <mi> Re </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> &#956; </mi> <mo> ) </mo> </mrow> <mo> &lt; </mo> <mn> 0 </mn> </mrow> <mo> &#8744; </mo> <mrow> <mi> &#956; </mi> <mo> &#8712; </mo> <msup> <mi> &#8469; </mi> <mo> + </mo> </msup> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <apply> <power /> <apply> <ci> Subscript </ci> <apply> <ci> LegendreQ </ci> <ci> &#120083; </ci> </apply> <ci> &#957; </ci> </apply> <ci> &#956; </ci> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <or /> <apply> <lt /> <apply> <real /> <ci> &#956; </ci> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <in /> <ci> &#956; </ci> <apply> <ci> SuperPlus </ci> <ci> &#8469; </ci> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LegendreP", "[", RowBox[List["\[Nu]_", ",", "\[Mu]_", ",", "3", ",", "1"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["0", "/;", RowBox[List[RowBox[List[RowBox[List["Re", "[", "\[Mu]", "]"]], "<", "0"]], "||", RowBox[List["(", RowBox[List[RowBox[List["\[Mu]", "\[Element]", "Integers"]], "&&", RowBox[List["\[Mu]", ">", "0"]]]], ")"]]]]]]]]]]


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





2001-10-29