LegendreQ[7, 6, 3, z] == (-(1/(z^2 - 1)^3)) (3 (15360 + 13 z^2 (-11895 + 11 z^2 (3335 - 5058 z^2 + 4158 z^4 - 1785 z^6 + 315 z^8)))) + (135135/2) z (z^2 - 1)^3 (Log[z + 1] - Log[z - 1])

Cell[BoxData[RowBox[List[RowBox[List["LegendreQ", "[", RowBox[List["7", ",", "6", ",", "3", ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["1", SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox["z", "2"], "-", "1"]], ")"]], "3"]]]], RowBox[List["(", RowBox[List["3", " ", RowBox[List["(", RowBox[List["15360", "+", RowBox[List["13", " ", SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "11895"]], "+", RowBox[List["11", " ", SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List["3335", "-", RowBox[List["5058", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["4158", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["1785", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["315", " ", SuperscriptBox["z", "8"]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], ")"]]]], "+", RowBox[List[FractionBox["135135", "2"], " ", "z", " ", SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox["z", "2"], "-", "1"]], ")"]], "3"], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", RowBox[List["z", "+", "1"]], "]"]], "-", RowBox[List["Log", "[", RowBox[List["z", "-", "1"]], "]"]]]], ")"]]]]]]]]]]

<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> &#120084; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[GothicCapitalQ]&quot;, LegendreQ] </annotation> </semantics> <mn> 7 </mn> <mn> 6 </mn> </msubsup> </mstyle> <mo> ( </mo> <mstyle scriptlevel='0'> <mi> z </mi> </mstyle> <mstyle scriptlevel='0'> <mo> ) </mo> </mstyle> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mfrac> <mn> 135135 </mn> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mfrac> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 13 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 11 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 315 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 1785 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4158 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 5058 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 3335 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 11895 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 15360 </mn> </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> 3 </mn> </msup> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <apply> <power /> <apply> <ci> Subscript </ci> <apply> <ci> LegendreQ </ci> <ci> &#120084; </ci> </apply> <cn type='integer'> 7 </cn> </apply> <cn type='integer'> 6 </cn> </apply> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> 135135 <sep /> 2 </cn> <ci> z </ci> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 3 </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 /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 13 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 11 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 315 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1785 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 4158 </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'> 5058 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 3335 </cn> </apply> </apply> <cn type='integer'> -11895 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 15360 </cn> </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'> 3 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LegendreQ", "[", RowBox[List["7", ",", "6", ",", "3", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["3", " ", RowBox[List["(", RowBox[List["15360", "+", RowBox[List["13", " ", SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "11895"]], "+", RowBox[List["11", " ", SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List["3335", "-", RowBox[List["5058", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["4158", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["1785", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["315", " ", SuperscriptBox["z", "8"]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox["z", "2"], "-", "1"]], ")"]], "3"]]]], "+", RowBox[List[FractionBox["135135", "2"], " ", "z", " ", SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox["z", "2"], "-", "1"]], ")"]], "3"], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", RowBox[List["z", "+", "1"]], "]"]], "-", RowBox[List["Log", "[", RowBox[List["z", "-", "1"]], "]"]]]], ")"]]]]]]]]]]

2001-10-29