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variants of this functions
LegendreP




Mathematica Notation

Traditional Notation









Hypergeometric Functions > LegendreP[nu,z] > Representations through equivalent functions > With related functions





http://functions.wolfram.com/07.07.27.0001.01









  


  








Input Form





LegendreQ[\[Nu] - 1/2, z]/LegendreP[\[Nu] - 1/2, z] - LegendreQ[\[Nu] + 1/2, z]/LegendreP[\[Nu] + 1/2, z] == 1/((\[Nu] + 1/2) LegendreP[\[Nu] - 1/2, z] LegendreP[\[Nu] + 1/2, z])








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[FractionBox[RowBox[List[" ", RowBox[List["LegendreQ", "[", RowBox[List[RowBox[List["\[Nu]", "-", FractionBox["1", "2"]]], ",", "z"]], "]"]]]], RowBox[List["LegendreP", "[", RowBox[List[RowBox[List["\[Nu]", "-", FractionBox["1", "2"]]], ",", "z"]], "]"]]], "-", FractionBox[RowBox[List["LegendreQ", "[", RowBox[List[RowBox[List["\[Nu]", "+", FractionBox["1", "2"]]], ",", "z"]], "]"]], RowBox[List["LegendreP", "[", RowBox[List[RowBox[List["\[Nu]", "+", FractionBox["1", "2"]]], ",", "z"]], "]"]]]]], "\[Equal]", FractionBox["1", RowBox[List[RowBox[List["(", RowBox[List["\[Nu]", "+", FractionBox["1", "2"]]], ")"]], " ", RowBox[List["LegendreP", "[", RowBox[List[RowBox[List["\[Nu]", "-", FractionBox["1", "2"]]], ",", "z"]], "]"]], " ", RowBox[List["LegendreP", "[", RowBox[List[RowBox[List["\[Nu]", "+", FractionBox["1", "2"]]], ",", "z"]], "]"]]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mfrac> <mrow> <msub> <semantics> <mi> Q </mi> <annotation encoding='Mathematica'> TagBox[&quot;Q&quot;, LegendreQ] </annotation> </semantics> <mrow> <mi> &#957; </mi> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mrow> <msub> <semantics> <mi> P </mi> <annotation encoding='Mathematica'> TagBox[&quot;P&quot;, LegendreP] </annotation> </semantics> <mrow> <mi> &#957; </mi> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mfrac> <mo> - </mo> <mfrac> <mrow> <msub> <semantics> <mi> Q </mi> <annotation encoding='Mathematica'> TagBox[&quot;Q&quot;, LegendreQ] </annotation> </semantics> <mrow> <mi> &#957; </mi> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mrow> <msub> <semantics> <mi> P </mi> <annotation encoding='Mathematica'> TagBox[&quot;P&quot;, LegendreP] </annotation> </semantics> <mrow> <mi> &#957; </mi> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mfrac> </mrow> <mo> &#10869; </mo> <mfrac> <mn> 1 </mn> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> &#957; </mi> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msub> <semantics> <mi> P </mi> <annotation encoding='Mathematica'> TagBox[&quot;P&quot;, LegendreP] </annotation> </semantics> <mrow> <mi> &#957; </mi> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msub> <semantics> <mi> P </mi> <annotation encoding='Mathematica'> TagBox[&quot;P&quot;, LegendreP] </annotation> </semantics> <mrow> <mi> &#957; </mi> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <plus /> <apply> <times /> <apply> <ci> LegendreQ </ci> <apply> <plus /> <ci> &#957; </ci> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <ci> z </ci> </apply> <apply> <power /> <apply> <ci> LegendreP </ci> <apply> <plus /> <ci> &#957; </ci> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ci> LegendreQ </ci> <apply> <plus /> <ci> &#957; </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> <apply> <power /> <apply> <ci> LegendreP </ci> <apply> <plus /> <ci> &#957; </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> &#957; </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> LegendreP </ci> <apply> <plus /> <ci> &#957; </ci> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <ci> z </ci> </apply> <apply> <ci> LegendreP </ci> <apply> <plus /> <ci> &#957; </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[FractionBox[RowBox[List["LegendreQ", "[", RowBox[List[RowBox[List["\[Nu]_", "-", FractionBox["1", "2"]]], ",", "z_"]], "]"]], RowBox[List["LegendreP", "[", RowBox[List[RowBox[List["\[Nu]_", "-", FractionBox["1", "2"]]], ",", "z_"]], "]"]]], "-", FractionBox[RowBox[List["LegendreQ", "[", RowBox[List[RowBox[List["\[Nu]_", "+", FractionBox["1", "2"]]], ",", "z_"]], "]"]], RowBox[List["LegendreP", "[", RowBox[List[RowBox[List["\[Nu]_", "+", FractionBox["1", "2"]]], ",", "z_"]], "]"]]]]], "]"]], "\[RuleDelayed]", FractionBox["1", RowBox[List[RowBox[List["(", RowBox[List["\[Nu]", "+", FractionBox["1", "2"]]], ")"]], " ", RowBox[List["LegendreP", "[", RowBox[List[RowBox[List["\[Nu]", "-", FractionBox["1", "2"]]], ",", "z"]], "]"]], " ", RowBox[List["LegendreP", "[", RowBox[List[RowBox[List["\[Nu]", "+", FractionBox["1", "2"]]], ",", "z"]], "]"]]]]]]]]]


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





2001-10-29