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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/07.12.03.0025.01









  


  










Input Form





LegendreQ[8, \[Mu], 3, z] == (((Pi Csc[Pi \[Mu]])/(2 Gamma[9 - \[Mu]])) E^(I Pi \[Mu]) ((z + 1)^\[Mu] (11025 + 2027025 z^8 - 2027025 z^7 \[Mu] - 12916 \[Mu]^2 + 1974 \[Mu]^4 - 84 \[Mu]^6 + \[Mu]^8 + 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 (-1260 + 1043 \[Mu]^2 - 100 \[Mu]^4 + 2 \[Mu]^6) - 9 z \[Mu] (-15159 + 4396 \[Mu]^2 - 266 \[Mu]^4 + 4 \[Mu]^6)) + (z - 1)^\[Mu] (-11025 - 2027025 z^8 - 2027025 z^7 \[Mu] + 12916 \[Mu]^2 - 1974 \[Mu]^4 + 84 \[Mu]^6 - \[Mu]^8 - 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 (-1260 + 1043 \[Mu]^2 - 100 \[Mu]^4 + 2 \[Mu]^6) - 9 z \[Mu] (-15159 + 4396 \[Mu]^2 - 266 \[Mu]^4 + 4 \[Mu]^6))))/ ((z - 1)^(\[Mu]/2) (z + 1)^(\[Mu]/2))










Standard Form





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MathML Form







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</mo> <msup> <mi> &#956; </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4396 </mn> <mo> &#8290; </mo> <msup> <mi> &#956; </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mn> 15159 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <msup> <mi> &#956; </mi> <mn> 8 </mn> </msup> <mo> - </mo> <mrow> <mn> 84 </mn> <mo> &#8290; </mo> <msup> <mi> &#956; </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1974 </mn> <mo> &#8290; </mo> <msup> <mi> &#956; </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 12916 </mn> <mo> &#8290; </mo> <msup> <mi> &#956; </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 11025 </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> 2027025 </mn> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 2027025 </mn> <mo> &#8290; 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Rule Form





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





2001-10-29