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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/07.12.06.0018.01









  


  










Input Form





LegendreQ[\[Nu], \[Mu], 3, z] == (-(Pi/2)) Csc[Pi \[Mu]]^2 E^(Pi I \[Mu]) ((Sin[Pi \[Nu]] ((1 - z)^\[Mu]/(z - 1)^\[Mu]) + Sin[Pi (\[Mu] - \[Nu])]) ((z - 1)^(\[Mu]/2)/(z + 1)^(\[Mu]/2)) (1/Gamma[1 - \[Mu]]) Hypergeometric2F1[-\[Nu], \[Nu] + 1, 1 - \[Mu], (1 + z)/2] + (Pi/(Gamma[-\[Mu] - \[Nu]] Gamma[1 - \[Mu] + \[Nu]])) (1 - Csc[Pi (\[Mu] + \[Nu])] Sin[Pi \[Nu]] ((z - 1)^\[Mu]/ (1 - z)^\[Mu])) ((z + 1)^(\[Mu]/2)/(z - 1)^(\[Mu]/2)) (1/Gamma[1 + \[Mu]]) Hypergeometric2F1[-\[Nu], \[Nu] + 1, 1 + \[Mu], (1 + z)/2]) /; !Element[\[Mu], Integers]










Standard Form





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MathML Form







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</ci> <integers /> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2001-10-29