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variants of this functions
LegendreQ






Mathematica Notation

Traditional Notation









Hypergeometric Functions > LegendreQ[nu,mu,2,z] > Representations through more general functions > Through hypergeometric functions > Involving 2F~1





http://functions.wolfram.com/07.11.26.0002.01









  


  










Input Form





LegendreQ[\[Nu], \[Mu], 2, z] == ((2^(-1 - \[Nu]) Pi Csc[Pi \[Mu]])/ Gamma[1 - \[Mu] + \[Nu]]) (1 + z)^(\[Nu] - \[Mu]/2) (1 - z)^(\[Mu]/2) (Cos[Pi \[Mu]] Gamma[1 - \[Mu] + \[Nu]] ((1 + z)^\[Mu]/(1 - z)^\[Mu]) Hypergeometric2F1Regularized[-\[Nu], -\[Mu] - \[Nu], 1 - \[Mu], (z - 1)/(z + 1)] - Gamma[1 + \[Mu] + \[Nu]] Hypergeometric2F1Regularized[-\[Nu], \[Mu] - \[Nu], 1 + \[Mu], (z - 1)/(z + 1)]) /; !Element[\[Mu], Integers] && !IntervalMemberQ[Interval[{-Infinity, -1}], 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





© 1998- Wolfram Research, Inc.