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   http://functions.wolfram.com/07.12.03.0101.01
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    LegendreQ[6, 1, 3, z] == (1/(80 Sqrt[z - 1] Sqrt[z + 1])) 
  (256 - 42 z^2 (103 - 260 z^2 + 165 z^4) + 
   105 z (-5 + 35 z^2 - 63 z^4 + 33 z^6) (Log[z + 1] - Log[z - 1])) 
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   Cell[BoxData[RowBox[List[RowBox[List["LegendreQ", "[", RowBox[List["6", ",", "1", ",", "3", ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["80", " ", SqrtBox[RowBox[List["z", "-", "1"]]], " ", SqrtBox[RowBox[List["z", "+", "1"]]]]]], RowBox[List["(", RowBox[List["256", "-", RowBox[List["42", " ", SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List["103", "-", RowBox[List["260", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["165", " ", SuperscriptBox["z", "4"]]]]], ")"]]]], "+", RowBox[List["105", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "5"]], "+", RowBox[List["35", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["63", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["33", " ", SuperscriptBox["z", "6"]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", RowBox[List["z", "+", "1"]], "]"]], "-", RowBox[List["Log", "[", RowBox[List["z", "-", "1"]], "]"]]]], ")"]]]]]], ")"]]]]]]]] 
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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> 6 </mn>  <mn> 1 </mn>  </msubsup>  </mstyle>  <mo> ( </mo>  <mstyle scriptlevel='0'>  <mi> z </mi>  </mstyle>  <mstyle scriptlevel='0'>  <mo> ) </mo>  </mstyle>  </mrow>  <mo> ⩵ </mo>  <mrow>  <mfrac>  <mn> 1 </mn>  <mrow>  <mn> 80 </mn>  <mo> ⁢ </mo>  <msqrt>  <mrow>  <mi> z </mi>  <mo> - </mo>  <mn> 1 </mn>  </mrow>  </msqrt>  <mo> ⁢ </mo>  <msqrt>  <mrow>  <mi> z </mi>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  </msqrt>  </mrow>  </mfrac>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mn> 256 </mn>  <mo> - </mo>  <mrow>  <mn> 42 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mn> 103 </mn>  <mo> - </mo>  <mrow>  <mn> 260 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 165 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 4 </mn>  </msup>  </mrow>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> + </mo>  <mrow>  <mn> 105 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mo> - </mo>  <mn> 5 </mn>  </mrow>  <mo> + </mo>  <mrow>  <mn> 35 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 63 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 4 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 33 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 6 </mn>  </msup>  </mrow>  </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>  <mi> z </mi>  <mo> - </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  </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'> 6 </cn>  </apply>  <cn type='integer'> 1 </cn>  </apply>  <ci> z </ci>  </apply>  <apply>  <times />  <apply>  <times />  <cn type='integer'> 1 </cn>  <apply>  <power />  <apply>  <times />  <cn type='integer'> 80 </cn>  <apply>  <power />  <apply>  <plus />  <ci> z </ci>  <cn type='integer'> -1 </cn>  </apply>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <apply>  <power />  <apply>  <plus />  <ci> z </ci>  <cn type='integer'> 1 </cn>  </apply>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <plus />  <cn type='integer'> 256 </cn>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 42 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  <apply>  <plus />  <cn type='integer'> 103 </cn>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 260 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 165 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 4 </cn>  </apply>  </apply>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 105 </cn>  <ci> z </ci>  <apply>  <plus />  <cn type='integer'> -5 </cn>  <apply>  <times />  <cn type='integer'> 35 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 63 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 4 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 33 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 6 </cn>  </apply>  </apply>  </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>  </apply>  </apply>  </annotation-xml>  </semantics>  </math> 
   
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  | Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LegendreQ", "[", RowBox[List["6", ",", "1", ",", "3", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["256", "-", RowBox[List["42", " ", SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List["103", "-", RowBox[List["260", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["165", " ", SuperscriptBox["z", "4"]]]]], ")"]]]], "+", RowBox[List["105", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "5"]], "+", RowBox[List["35", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["63", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["33", " ", SuperscriptBox["z", "6"]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", RowBox[List["z", "+", "1"]], "]"]], "-", RowBox[List["Log", "[", RowBox[List["z", "-", "1"]], "]"]]]], ")"]]]]]], RowBox[List["80", " ", SqrtBox[RowBox[List["z", "-", "1"]]], " ", SqrtBox[RowBox[List["z", "+", "1"]]]]]]]]]]  |  
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   Date Added to functions.wolfram.com (modification date)
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