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http://functions.wolfram.com/07.12.03.0042.01
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LegendreQ[0, 8, 3, z] == (40320 (z + 7 z^3 + 7 z^5 + z^7))/(z^2 - 1)^4
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Cell[BoxData[RowBox[List[RowBox[List["LegendreQ", "[", RowBox[List["0", ",", "8", ",", "3", ",", "z"]], "]"]], "\[Equal]", FractionBox[RowBox[List["40320", " ", RowBox[List["(", RowBox[List["z", "+", RowBox[List["7", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["7", " ", SuperscriptBox["z", "5"]]], "+", SuperscriptBox["z", "7"]]], ")"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox["z", "2"], "-", "1"]], ")"]], "4"]]]]]]
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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> <mstyle scriptlevel='0'> <msubsup> <semantics> <mi> 𝔔 </mi> <annotation encoding='Mathematica'> TagBox["\[GothicCapitalQ]", LegendreQ] </annotation> </semantics> <mn> 0 </mn> <mn> 8 </mn> </msubsup> </mstyle> <mo> ( </mo> <mstyle scriptlevel='0'> <mi> z </mi> </mstyle> <mstyle scriptlevel='0'> <mo> ) </mo> </mstyle> </mrow> <mo> ⩵ </mo> <mfrac> <mrow> <mn> 40320 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mrow> <mn> 7 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 7 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <msup> <mrow> <mo> ( </mo> <mrow> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 4 </mn> </msup> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <apply> <power /> <apply> <ci> Subscript </ci> <apply> <ci> LegendreQ </ci> <ci> 𝔔 </ci> </apply> <cn type='integer'> 0 </cn> </apply> <cn type='integer'> 8 </cn> </apply> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> 40320 </cn> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> 7 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 7 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 4 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LegendreQ", "[", RowBox[List["0", ",", "8", ",", "3", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["40320", " ", RowBox[List["(", RowBox[List["z", "+", RowBox[List["7", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["7", " ", SuperscriptBox["z", "5"]]], "+", SuperscriptBox["z", "7"]]], ")"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox["z", "2"], "-", "1"]], ")"]], "4"]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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