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variants of this functions
LegendreQ




Mathematica Notation

Traditional Notation









Hypergeometric Functions > LegendreQ[nu,mu,3,z] > Series representations > Generalized power series > Expansions at z==1





http://functions.wolfram.com/07.12.06.0005.01









  


  








Input Form





LegendreQ[\[Nu], \[Mu], 3, z] == (Pi/2) Csc[\[Mu] Pi] E^(Pi I \[Mu]) (((z + 1)^(\[Mu]/2)/(z - 1)^(\[Mu]/2)) (1/Gamma[1 - \[Mu]]) Sum[((Pochhammer[-\[Nu], k] Pochhammer[\[Nu] + 1, k])/ (Pochhammer[1 - \[Mu], k] k!)) ((1 - z)/2)^k, {k, 0, Infinity}] - ((z - 1)^(\[Mu]/2)/(z + 1)^(\[Mu]/2)) (Pochhammer[\[Nu] - \[Mu] + 1, 2 \[Mu]]/Gamma[1 + \[Mu]]) Sum[((Pochhammer[-\[Nu], k] Pochhammer[\[Nu] + 1, k])/ (Pochhammer[1 + \[Mu], k] k!)) ((1 - z)/2)^k, {k, 0, Infinity}]) /; Abs[(1 - z)/2] < 1 && !Element[\[Mu], Integers]








Standard Form





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MathML Form







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Rule Form





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





2001-10-29