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variants of this functions
LegendreQ






Mathematica Notation

Traditional Notation









Hypergeometric Functions > LegendreQ[nu,mu,2,z] > Series representations > Generalized power series > Expansions at z==-1





http://functions.wolfram.com/07.11.06.0020.01









  


  










Input Form





LegendreQ[\[Nu], \[Mu], 2, z] == ((1/(2 Pi)) Sin[Pi (\[Mu] - \[Nu])] Sin[Pi \[Nu]] Sin[Pi (\[Mu] + \[Nu])] Csc[Pi \[Mu]] Gamma[1 + \[Mu] + \[Nu]] ((1 - z)^\[Mu] (Cos[Pi \[Mu]] Csc[Pi (\[Mu] - \[Nu])] + Csc[Pi \[Nu]]) Gamma[\[Mu]] Gamma[-\[Mu] - \[Nu]] Hypergeometric2F1[-\[Nu], 1 + \[Nu], 1 - \[Mu], (1 + z)/2] - (1 + z)^\[Mu] (Cos[Pi \[Mu]] Csc[Pi \[Nu]] - Csc[Pi (\[Mu] + \[Nu])]) Gamma[-\[Mu]] Gamma[\[Mu] - \[Nu]] Hypergeometric2F1[-\[Nu], 1 + \[Nu], 1 + \[Mu], (1 + z)/2]))/ (1 - z^2)^(\[Mu]/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





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