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variants of this functions
LegendreP




Mathematica Notation

Traditional Notation









Polynomials > LegendreP[n,z] > Specific values > Specialized values > For fixed z





http://functions.wolfram.com/05.03.03.0014.01









  


  








Input Form





LegendreP[10, z] == (1/256) (46189 z^10 - 109395 z^8 + 90090 z^6 - 30030 z^4 + 3465 z^2 - 63)








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["LegendreP", "[", RowBox[List["10", ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "256"], " ", RowBox[List["(", RowBox[List[RowBox[List["46189", " ", SuperscriptBox["z", "10"]]], "-", RowBox[List["109395", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["90090", " ", SuperscriptBox["z", "6"]]], "-", RowBox[List["30030", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["3465", " ", SuperscriptBox["z", "2"]]], "-", "63"]], ")"]]]]]]]]








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> <semantics> <mi> P </mi> <annotation encoding='Mathematica'> TagBox[&quot;P&quot;, LegendreP] </annotation> </semantics> <mn> 10 </mn> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 256 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 46189 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 10 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 109395 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 90090 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 30030 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 3465 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mn> 63 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> LegendreP </ci> <cn type='integer'> 10 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 256 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 46189 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 10 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 109395 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 90090 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 30030 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 3465 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -63 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LegendreP", "[", RowBox[List["10", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "256"], " ", RowBox[List["(", RowBox[List[RowBox[List["46189", " ", SuperscriptBox["z", "10"]]], "-", RowBox[List["109395", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["90090", " ", SuperscriptBox["z", "6"]]], "-", RowBox[List["30030", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["3465", " ", SuperscriptBox["z", "2"]]], "-", "63"]], ")"]]]]]]]]


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





2001-10-29