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variants of this functions
LegendreP






Mathematica Notation

Traditional Notation









Hypergeometric Functions > LegendreP[nu,mu,2,z] > Specific values > Specialized values > For fixed z





http://functions.wolfram.com/07.08.03.0049.01









  


  










Input Form





LegendreP[6, 1, 2, z] == (-(21/8)) z Sqrt[1 - z^2] (5 - 30 z^2 + 33 z^4)










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["LegendreP", "[", RowBox[List["6", ",", "1", ",", "2", ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox["21", "8"]]], " ", "z", " ", SqrtBox[RowBox[List["1", "-", SuperscriptBox["z", "2"]]]], " ", RowBox[List["(", RowBox[List["5", "-", RowBox[List["30", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["33", " ", SuperscriptBox["z", "4"]]]]], ")"]]]]]]]]










MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msubsup> <semantics> <mi> P </mi> <annotation encoding='Mathematica'> TagBox[&quot;P&quot;, LegendreP] </annotation> </semantics> <mn> 6 </mn> <mn> 1 </mn> </msubsup> <mo> ( </mo> <semantics> <mi> z </mi> <annotation encoding='Mathematica'> TagBox[&quot;z&quot;, HoldComplete[LegendreP, 2]] </annotation> </semantics> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 21 </mn> <mn> 8 </mn> </mfrac> </mrow> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 33 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 30 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> LegendreP </ci> <cn type='integer'> 6 </cn> <cn type='integer'> 1 </cn> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 21 <sep /> 8 </cn> </apply> <ci> z </ci> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 33 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 30 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 5 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LegendreP", "[", RowBox[List["6", ",", "1", ",", "2", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["-", "21"]], ")"]], " ", "z", " ", SqrtBox[RowBox[List["1", "-", SuperscriptBox["z", "2"]]]], " ", RowBox[List["(", RowBox[List["5", "-", RowBox[List["30", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["33", " ", SuperscriptBox["z", "4"]]]]], ")"]]]]]]]]










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





2001-10-29