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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/07.11.06.0037.01









  


  










Input Form





LegendreQ[\[Nu], m, 2, z] == (2^(-\[Nu] - 2)/(Sqrt[Pi] Gamma[-m - \[Nu]] Gamma[1 - m + \[Nu]])) (z - 1)^(-\[Nu] - 1) ((1 + z)^(m/2)/(1 - z)^(m/2)) (2^(2 \[Nu] + 1) Gamma[-m - \[Nu]] Gamma[1/2 + \[Nu]] (z - 1)^(2 \[Nu] + 1) (Log[1 + z] - Log[-z - 1]) Hypergeometric2F1[-\[Nu], m - \[Nu], -2 \[Nu], 2/(1 - z)] + Gamma[-(1/2) - \[Nu]] Gamma[1 - m + \[Nu]] (2 Pi Cot[Pi \[Nu]] + Log[1 + z] - Log[-z - 1]) Hypergeometric2F1[1 + \[Nu], 1 + m + \[Nu], 2 + 2 \[Nu], 2/(1 - z)]) /; !IntervalMemberQ[Interval[{-1, 1}], z] && Element[m, Integers] && m >= 0










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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