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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==infinity





http://functions.wolfram.com/07.11.06.0031.01









  


  










Input Form





LegendreQ[\[Nu], \[Mu], 2, z] == 2^(-2 - \[Nu]) E^(I Pi \[Mu]) z^(-1 - \[Mu] - \[Nu]) (1 - z^2)^(\[Mu]/2) Sqrt[Pi] Sec[Pi \[Nu]] ((Cos[Pi (\[Mu] + \[Nu])] + E^(I Pi (\[Nu] - \[Mu]))) Gamma[1 + \[Mu] + \[Nu]] Hypergeometric2F1Regularized[ (1 + \[Mu] + \[Nu])/2, 1 + (\[Mu] + \[Nu])/2, 3/2 + \[Nu], 1/z^2] + I 2^(1 + 2 \[Nu]) Sin[Pi (\[Mu] - \[Nu])] z^(1 + 2 \[Nu]) Gamma[\[Mu] - \[Nu]] Hypergeometric2F1Regularized[(\[Mu] - \[Nu])/2, (1 + \[Mu] - \[Nu])/2, 1/2 - \[Nu], 1/z^2]) /; Im[z] > 0 || IntervalMemberQ[Interval[{-Infinity, -1}], z] || IntervalMemberQ[Interval[{0, Infinity}], z]










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





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