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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 mu, z





http://functions.wolfram.com/07.11.03.0022.01









  


  










Input Form





LegendreQ[8, \[Mu], 2, z] == (((Pi Csc[Pi \[Mu]])/(2 Gamma[9 - \[Mu]])) ((1 + z)^\[Mu] (2027025 z^8 - 2027025 z^7 \[Mu] + (-7 + \[Mu]) (-5 + \[Mu]) (-3 + \[Mu]) (-1 + \[Mu]) (1 + \[Mu]) (3 + \[Mu]) (5 + \[Mu]) (7 + \[Mu]) + 945945 z^6 (-4 + \[Mu]^2) - 135135 z^5 \[Mu] (-23 + 2 \[Mu]^2) + 51975 z^4 (42 - 22 \[Mu]^2 + \[Mu]^4) - 3465 z^3 \[Mu] (383 - 70 \[Mu]^2 + 2 \[Mu]^4) + 315 z^2 (-6 + \[Mu]) (6 + \[Mu]) (35 - 28 \[Mu]^2 + 2 \[Mu]^4) - 9 z \[Mu] (-15159 + 4396 \[Mu]^2 - 266 \[Mu]^4 + 4 \[Mu]^6)) Cos[Pi \[Mu]] - (1 - z)^\[Mu] (2027025 z^8 + 2027025 z^7 \[Mu] + (-7 + \[Mu]) (-5 + \[Mu]) (-3 + \[Mu]) (-1 + \[Mu]) (1 + \[Mu]) (3 + \[Mu]) (5 + \[Mu]) (7 + \[Mu]) + 945945 z^6 (-4 + \[Mu]^2) + 135135 z^5 \[Mu] (-23 + 2 \[Mu]^2) + 51975 z^4 (42 - 22 \[Mu]^2 + \[Mu]^4) + 3465 z^3 \[Mu] (383 - 70 \[Mu]^2 + 2 \[Mu]^4) + 315 z^2 (-6 + \[Mu]) (6 + \[Mu]) (35 - 28 \[Mu]^2 + 2 \[Mu]^4) + 9 z \[Mu] (-15159 + 4396 \[Mu]^2 - 266 \[Mu]^4 + 4 \[Mu]^6)) Csc[Pi \[Mu]]))/(1 - z^2)^(\[Mu]/2)










Standard Form





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MathML Form







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</mi> <mo> - </mo> <mn> 7 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> &#956; </mi> <mo> - </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> &#956; </mi> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> &#956; </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> &#956; </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> &#956; </mi> <mo> + </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> &#956; </mi> <mo> + </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> &#956; </mi> <mo> + </mo> <mn> 7 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> &#960; </mi> <mo> &#8290; </mo> <mi> &#956; </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mi> &#956; </mi> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2027025 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2027025 </mn> <mo> &#8290; </mo> <mi> &#956; </mi> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 945945 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> &#956; </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 135135 </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> 23 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 51975 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> &#956; </mi> <mn> 4 </mn> </msup> <mo> - </mo> <mrow> <mn> 22 </mn> <mo> &#8290; </mo> <msup> <mi> &#956; </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 42 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 3465 </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> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 70 </mn> <mo> &#8290; </mo> <msup> <mi> &#956; </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 383 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 315 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> &#956; </mi> <mo> - </mo> <mn> 6 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; 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Rule Form





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





2001-10-29





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