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variants of this functions
LegendreQ






Mathematica Notation

Traditional Notation









Hypergeometric Functions > LegendreQ[nu,mu,3,z] > Specific values > Specialized values > For fixed mu, z





http://functions.wolfram.com/07.12.03.0027.01









  


  










Input Form





LegendreQ[10, \[Mu], 3, z] == (((Pi Csc[Pi \[Mu]])/(2 Gamma[11 - \[Mu]])) E^(I Pi \[Mu]) ((z + 1)^\[Mu] (-893025 + 654729075 z^10 - 654729075 z^9 \[Mu] + 1057221 \[Mu]^2 - 172810 \[Mu]^4 + 8778 \[Mu]^6 - 165 \[Mu]^8 + \[Mu]^10 + 310134825 z^8 (-5 + \[Mu]^2) - 45945900 z^7 \[Mu] (-29 + 2 \[Mu]^2) - 2837835 z^5 \[Mu] (314 - 45 \[Mu]^2 + \[Mu]^4) + 9459450 z^6 (135 - 56 \[Mu]^2 + 2 \[Mu]^4) + 315315 z^4 (-1350 + 874 \[Mu]^2 - 65 \[Mu]^4 + \[Mu]^6) - 12870 z^3 \[Mu] (-16830 + 3773 \[Mu]^2 - 175 \[Mu]^4 + 2 \[Mu]^6) - 55 z \[Mu] (251865 - 78877 \[Mu]^2 + 5754 \[Mu]^4 - 138 \[Mu]^6 + \[Mu]^8) + 1485 z^2 (33075 - 29828 \[Mu]^2 + 3479 \[Mu]^4 - 112 \[Mu]^6 + \[Mu]^8)) + (z - 1)^\[Mu] (893025 - 654729075 z^10 - 654729075 z^9 \[Mu] - 1057221 \[Mu]^2 + 172810 \[Mu]^4 - 8778 \[Mu]^6 + 165 \[Mu]^8 - \[Mu]^10 - 310134825 z^8 (-5 + \[Mu]^2) - 45945900 z^7 \[Mu] (-29 + 2 \[Mu]^2) - 2837835 z^5 \[Mu] (314 - 45 \[Mu]^2 + \[Mu]^4) - 9459450 z^6 (135 - 56 \[Mu]^2 + 2 \[Mu]^4) - 315315 z^4 (-1350 + 874 \[Mu]^2 - 65 \[Mu]^4 + \[Mu]^6) - 12870 z^3 \[Mu] (-16830 + 3773 \[Mu]^2 - 175 \[Mu]^4 + 2 \[Mu]^6) - 55 z \[Mu] (251865 - 78877 \[Mu]^2 + 5754 \[Mu]^4 - 138 \[Mu]^6 + \[Mu]^8) - 1485 z^2 (33075 - 29828 \[Mu]^2 + 3479 \[Mu]^4 - 112 \[Mu]^6 + \[Mu]^8))))/((z - 1)^(\[Mu]/2) (z + 1)^(\[Mu]/2))










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["LegendreQ", "[", RowBox[List["10", ",", "\[Mu]", ",", "3", ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["\[Pi]", " ", RowBox[List["Csc", "[", RowBox[List["\[Pi]", " ", "\[Mu]"]], "]"]]]], RowBox[List["2", " ", RowBox[List["Gamma", "[", RowBox[List["11", "-", "\[Mu]"]], "]"]]]]], SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "\[Pi]", " ", "\[Mu]"]]], SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", "1"]], ")"]], RowBox[List[RowBox[List["-", "\[Mu]"]], "/", "2"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "+", "1"]], ")"]], RowBox[List[RowBox[List["-", "\[Mu]"]], "/", "2"]]], RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["z", "+", "1"]], ")"]], "\[Mu]"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "893025"]], "+", RowBox[List["654729075", " ", SuperscriptBox["z", "10"]]], "-", RowBox[List["654729075", " ", SuperscriptBox["z", "9"], " ", 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MathML Form







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</mi> <mo> &#8290; </mo> <mi> &#960; </mi> <mo> &#8290; </mo> <mi> &#956; </mi> </mrow> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mrow> <mo> - </mo> <mi> &#956; </mi> </mrow> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mrow> <mo> - </mo> <mi> &#956; </mi> </mrow> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> &#956; </mi> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 654729075 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 10 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 654729075 </mn> <mo> &#8290; </mo> <mi> &#956; </mi> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 9 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 310134825 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> &#956; </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 45945900 </mn> <mo> &#8290; </mo> <mi> &#956; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msup> <mi> &#956; </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mn> 29 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 9459450 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msup> <mi> &#956; </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 56 </mn> <mo> &#8290; </mo> <msup> <mi> &#956; </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 135 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 2837835 </mn> <mo> &#8290; </mo> <mi> &#956; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> &#956; </mi> <mn> 4 </mn> </msup> <mo> - </mo> <mrow> <mn> 45 </mn> <mo> &#8290; </mo> <msup> <mi> &#956; </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 314 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 315315 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> &#956; </mi> <mn> 6 </mn> </msup> <mo> - </mo> <mrow> <mn> 65 </mn> <mo> &#8290; </mo> <msup> <mi> &#956; </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 874 </mn> <mo> &#8290; </mo> <msup> <mi> &#956; </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mn> 1350 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 12870 </mn> <mo> &#8290; </mo> <mi> &#956; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msup> <mi> &#956; </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 175 </mn> <mo> &#8290; </mo> <msup> <mi> &#956; </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 3773 </mn> <mo> &#8290; </mo> <msup> <mi> &#956; </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mn> 16830 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1485 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> &#956; </mi> <mn> 8 </mn> </msup> <mo> - </mo> <mrow> <mn> 112 </mn> <mo> &#8290; </mo> <msup> <mi> &#956; </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 3479 </mn> <mo> &#8290; </mo> <msup> <mi> &#956; </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 29828 </mn> <mo> &#8290; </mo> <msup> <mi> &#956; </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 33075 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 55 </mn> <mo> &#8290; </mo> <mi> &#956; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> &#956; </mi> <mn> 8 </mn> </msup> <mo> - </mo> <mrow> <mn> 138 </mn> <mo> &#8290; </mo> <msup> <mi> &#956; </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 5754 </mn> <mo> &#8290; </mo> <msup> <mi> &#956; </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 78877 </mn> <mo> &#8290; </mo> <msup> <mi> &#956; </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 251865 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <msup> <mi> &#956; </mi> <mn> 10 </mn> </msup> <mo> - </mo> <mrow> <mn> 165 </mn> <mo> &#8290; </mo> <msup> <mi> &#956; </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 8778 </mn> <mo> &#8290; </mo> <msup> <mi> &#956; </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 172810 </mn> <mo> &#8290; </mo> <msup> <mi> &#956; </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1057221 </mn> <mo> &#8290; </mo> <msup> <mi> &#956; </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mn> 893025 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> &#956; </mi> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 654729075 </mn> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 10 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 654729075 </mn> <mo> &#8290; </mo> <mi> &#956; </mi> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 9 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 310134825 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> &#956; </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 45945900 </mn> <mo> &#8290; </mo> <mi> &#956; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msup> <mi> &#956; </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mn> 29 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 9459450 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; 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Date Added to functions.wolfram.com (modification date)





2001-10-29





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