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http://functions.wolfram.com/07.10.03.0012.01
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LegendreQ[6, z] == (1/160) (-14 z (33 - 170 z^2 + 165 z^4) +
5 (-5 + 21 z^2 (5 - 15 z^2 + 11 z^4)) (Log[1 + z] - Log[1 - z]))
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Cell[BoxData[RowBox[List[RowBox[List["LegendreQ", "[", RowBox[List["6", ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "160"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "14"]], " ", "z", " ", RowBox[List["(", RowBox[List["33", "-", RowBox[List["170", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["165", " ", SuperscriptBox["z", "4"]]]]], ")"]]]], "+", RowBox[List["5", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "5"]], "+", RowBox[List["21", " ", SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List["5", "-", RowBox[List["15", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["11", " ", SuperscriptBox["z", "4"]]]]], ")"]]]]]], ")"]], RowBox[List["(", " ", RowBox[List[RowBox[List["Log", "[", RowBox[List["1", "+", "z"]], "]"]], "-", RowBox[List["Log", "[", RowBox[List["1", "-", "z"]], "]"]]]], ")"]]]]]], ")"]]]]]]]]
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<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> Q </mi> <annotation encoding='Mathematica'> TagBox["Q", LegendreQ] </annotation> </semantics> <mn> 6 </mn> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 160 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 21 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 11 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 15 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 14 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 165 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 170 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 33 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> LegendreQ </ci> <cn type='integer'> 6 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 160 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 5 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 21 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 11 </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'> 15 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 5 </cn> </apply> </apply> <cn type='integer'> -5 </cn> </apply> <apply> <plus /> <apply> <ln /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ln /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 14 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 165 </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'> 170 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 33 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LegendreQ", "[", RowBox[List["6", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "160"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "14"]], " ", "z", " ", RowBox[List["(", RowBox[List["33", "-", RowBox[List["170", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["165", " ", SuperscriptBox["z", "4"]]]]], ")"]]]], "+", RowBox[List["5", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "5"]], "+", RowBox[List["21", " ", SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List["5", "-", RowBox[List["15", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["11", " ", SuperscriptBox["z", "4"]]]]], ")"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", RowBox[List["1", "+", "z"]], "]"]], "-", RowBox[List["Log", "[", RowBox[List["1", "-", "z"]], "]"]]]], ")"]]]]]], ")"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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