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 LegendreQ

 http://functions.wolfram.com/07.12.03.0022.01

 Input Form

 LegendreQ[5, \[Mu], 3, z] == (((Pi Csc[Pi \[Mu]])/(2 Gamma[6 - \[Mu]])) E^(I Pi \[Mu]) ((z + 1)^\[Mu] (945 z^5 - 945 z^4 \[Mu] - (-4 + \[Mu]) (-2 + \[Mu]) \[Mu] (2 + \[Mu]) (4 + \[Mu]) - 105 z^2 \[Mu] (-7 + \[Mu]^2) + 210 z^3 (-5 + 2 \[Mu]^2) + 15 z (15 - 13 \[Mu]^2 + \[Mu]^4)) - (z - 1)^\[Mu] (945 z^5 + 64 \[Mu] + 945 z^4 \[Mu] - 20 \[Mu]^3 + \[Mu]^5 + 105 z^2 \[Mu] (-7 + \[Mu]^2) + 210 z^3 (-5 + 2 \[Mu]^2) + 15 z (15 - 13 \[Mu]^2 + \[Mu]^4))))/((z - 1)^(\[Mu]/2) (z + 1)^(\[Mu]/2))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["LegendreQ", "[", RowBox[List["5", ",", "\[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["6", "-", "\[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["945", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["945", " ", SuperscriptBox["z", "4"], " ", "\[Mu]"]], "-", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "4"]], "+", "\[Mu]"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", "\[Mu]"]], ")"]], " ", "\[Mu]", " ", RowBox[List["(", RowBox[List["2", "+", "\[Mu]"]], ")"]], " ", RowBox[List["(", RowBox[List["4", "+", "\[Mu]"]], ")"]]]], "-", RowBox[List["105", " ", SuperscriptBox["z", "2"], " ", "\[Mu]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "7"]], "+", SuperscriptBox["\[Mu]", "2"]]], ")"]]]], "+", RowBox[List["210", " ", SuperscriptBox["z", "3"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "5"]], "+", RowBox[List["2", " ", SuperscriptBox["\[Mu]", "2"]]]]], ")"]]]], "+", RowBox[List["15", " ", "z", " ", RowBox[List["(", RowBox[List["15", "-", RowBox[List["13", " ", SuperscriptBox["\[Mu]", "2"]]], "+", SuperscriptBox["\[Mu]", "4"]]], ")"]]]]]], ")"]]]], "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", "1"]], ")"]], "\[Mu]"], " ", RowBox[List["(", RowBox[List[RowBox[List["945", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["64", " ", "\[Mu]"]], "+", RowBox[List["945", " ", SuperscriptBox["z", "4"], " ", "\[Mu]"]], "-", RowBox[List["20", " ", SuperscriptBox["\[Mu]", "3"]]], "+", SuperscriptBox["\[Mu]", "5"], "+", RowBox[List["105", " ", SuperscriptBox["z", "2"], " ", "\[Mu]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "7"]], "+", SuperscriptBox["\[Mu]", "2"]]], ")"]]]], "+", RowBox[List["210", " ", SuperscriptBox["z", "3"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "5"]], "+", RowBox[List["2", " ", SuperscriptBox["\[Mu]", "2"]]]]], ")"]]]], "+", RowBox[List["15", " ", "z", " ", RowBox[List["(", RowBox[List["15", "-", RowBox[List["13", " ", SuperscriptBox["\[Mu]", "2"]]], "+", SuperscriptBox["\[Mu]", "4"]]], ")"]]]]]], ")"]]]]]], ")"]]]]]]]]

 MathML Form

 𝔔 TagBox["\[GothicCapitalQ]", LegendreQ] 5 μ ( z ) π csc ( π μ ) 2 Γ ( 6 - μ ) π μ ( z - 1 ) - μ / 2 ( z + 1 ) - μ / 2 ( ( z + 1 ) μ ( 945 z 5 - 945 μ z 4 + 210 ( 2 μ 2 - 5 ) z 3 - 105 μ ( μ 2 - 7 ) z 2 + 15 ( μ 4 - 13 μ 2 + 15 ) z - ( μ - 4 ) ( μ - 2 ) μ ( μ + 2 ) ( μ + 4 ) ) - ( z - 1 ) μ ( 945 z 5 + 945 μ z 4 + 210 ( 2 μ 2 - 5 ) z 3 + 105 μ ( μ 2 - 7 ) z 2 + 15 ( μ 4 - 13 μ 2 + 15 ) z + μ 5 - 20 μ 3 + 64 μ ) ) Subscript LegendreQ 𝔔 5 μ z μ 2 Gamma 6 -1 μ -1 μ z -1 -1 μ 2 -1 z 1 -1 μ 2 -1 z 1 μ 945 z 5 -1 945 μ z 4 210 2 μ 2 -5 z 3 -1 105 μ μ 2 -7 z 2 15 μ 4 -1 13 μ 2 15 z -1 μ -4 μ -2 μ μ 2 μ 4 -1 z -1 μ 945 z 5 945 μ z 4 210 2 μ 2 -5 z 3 105 μ μ 2 -7 z 2 15 μ 4 -1 13 μ 2 15 z μ 5 -1 20 μ 3 64 μ [/itex]

 Rule Form

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

 2001-10-29