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variants of this functions
LegendreP




Mathematica Notation

Traditional Notation









Polynomials > LegendreP[n,z] > Inequalities





http://functions.wolfram.com/05.03.29.0001.01









  


  








Input Form





Abs[LegendreP[n, Cos[\[Theta]]]] < Sqrt[2/(Pi n Sin[\[Theta]])] /; Element[n, Integers] && n > 0








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Abs", "[", RowBox[List["LegendreP", "[", RowBox[List["n", ",", " ", RowBox[List["Cos", "[", "\[Theta]", "]"]]]], "]"]], "]"]], "<", SqrtBox[FractionBox["2", RowBox[List["\[Pi]", " ", "n", " ", RowBox[List["Sin", "[", "\[Theta]", "]"]]]]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", ">", "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> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[LeftBracketingBar]&quot; </annotation> </semantics> <mrow> <msub> <semantics> <mi> P </mi> <annotation encoding='Mathematica'> TagBox[&quot;P&quot;, LegendreP] </annotation> </semantics> <mi> n </mi> </msub> <mo> ( </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> &#952; </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[RightBracketingBar]&quot; </annotation> </semantics> </mrow> <mo> &lt; </mo> <msqrt> <mfrac> <mn> 2 </mn> <mrow> <mi> &#960; </mi> <mo> &#8290; </mo> <mi> n </mi> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> &#952; </mi> <mo> ) </mo> </mrow> </mrow> </mfrac> </msqrt> </mrow> <mo> /; </mo> <mrow> <mi> n </mi> <mo> &#8712; </mo> <msup> <mi> &#8469; </mi> <mo> + </mo> </msup> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <lt /> <apply> <abs /> <apply> <ci> LegendreP </ci> <ci> n </ci> <apply> <cos /> <ci> &#952; </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <times /> <pi /> <ci> n </ci> <apply> <sin /> <ci> &#952; </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <in /> <ci> n </ci> <apply> <ci> SuperPlus </ci> <ci> &#8469; </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Abs", "[", RowBox[List["LegendreP", "[", RowBox[List["n", ",", RowBox[List["Cos", "[", "\[Theta]", "]"]]]], "]"]], "]"]], "<", SqrtBox[FractionBox["2", RowBox[List["\[Pi]", " ", "n", " ", RowBox[List["Sin", "[", "\[Theta]", "]"]]]]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", ">", "0"]]]]]]]]


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





2002-12-18