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variants of this functions
LegendreQ






Mathematica Notation

Traditional Notation









Hypergeometric Functions > LegendreQ[nu,mu,2,z] > Specific values > Specialized values > For fixed z





http://functions.wolfram.com/07.11.03.0119.01









  


  










Input Form





LegendreQ[8, 0, 2, z] == (1/8960) (30318 z - 294910 z^3 + 690690 z^5 - 450450 z^7 + 35 (35 - 1260 z^2 + 6930 z^4 - 12012 z^6 + 6435 z^8) (Log[1 + z] - Log[1 - z]))










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["LegendreQ", "[", RowBox[List["8", ",", "0", ",", "2", ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "8960"], RowBox[List["(", RowBox[List[RowBox[List["30318", " ", "z"]], "-", RowBox[List["294910", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["690690", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["450450", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["35", " ", RowBox[List["(", RowBox[List["35", "-", RowBox[List["1260", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["6930", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["12012", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["6435", " ", SuperscriptBox["z", "8"]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", RowBox[List["1", "+", "z"]], "]"]], "-", RowBox[List["Log", "[", RowBox[List["1", "-", "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> <mstyle scriptlevel='0'> <msubsup> <semantics> <mi> Q </mi> <annotation encoding='Mathematica'> TagBox[&quot;Q&quot;, LegendreQ] </annotation> </semantics> <mn> 8 </mn> <mn> 0 </mn> </msubsup> </mstyle> <mo> ( </mo> <mstyle scriptlevel='0'> <mi> z </mi> </mstyle> <mstyle scriptlevel='0'> <mo> ) </mo> </mstyle> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 8960 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 450450 </mn> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 690690 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 294910 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 30318 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 35 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 6435 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 12012 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 6930 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 1260 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 35 </mn> </mrow> <mo> ) </mo> </mrow> <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> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </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'> 8 </cn> <cn type='integer'> 0 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 8960 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -450450 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 690690 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 294910 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 30318 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> 35 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 6435 </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'> 12012 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 6930 </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'> 1260 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 35 </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> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LegendreQ", "[", RowBox[List["8", ",", "0", ",", "2", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["30318", " ", "z"]], "-", RowBox[List["294910", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["690690", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["450450", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["35", " ", RowBox[List["(", RowBox[List["35", "-", RowBox[List["1260", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["6930", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["12012", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["6435", " ", SuperscriptBox["z", "8"]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", RowBox[List["1", "+", "z"]], "]"]], "-", RowBox[List["Log", "[", RowBox[List["1", "-", "z"]], "]"]]]], ")"]]]]]], "8960"]]]]]










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





2001-10-29





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