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variants of this functions
LegendreQ






Mathematica Notation

Traditional Notation









Hypergeometric Functions > LegendreQ[nu,z] > Representations through more general functions > Through hypergeometric functions > Involving 2F1





http://functions.wolfram.com/07.10.26.0004.01









  


  










Input Form





LegendreQ[n, z] == (-1)^n ((1/2) (Log[1 + z] - Log[1 - z]) + PolyGamma[n + 1]) Hypergeometric2F1[-n, n + 1, 1, (z + 1)/2] - (-1)^n Sum[(((n + k)! PolyGamma[k + 1])/(k!^2 (n - k)!)) (-((z + 1)/2))^k, {k, 0, n}] /; Element[n, Integers] && n >= 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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