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variants of this functions
LegendreQ




Mathematica Notation

Traditional Notation









Hypergeometric Functions > LegendreQ[nu,z] > Representations through more general functions > Through Meijer G > Classical cases for the direct function itself





http://functions.wolfram.com/07.10.26.0007.01









  


  








Input Form





LegendreQ[\[Nu], z] == (-(Sin[Pi \[Nu]]/(2 Pi))) (Log[1 + z] - Log[1 - z] - 2 PolyGamma[1 + \[Nu]]) MeijerG[{{\[Nu] + 1, -\[Nu]}, {}}, {{0}, {0}}, (z - 1)/2] - (Sin[Pi \[Nu]]/(2 Pi^2 I)) Integrate[(((Gamma[s] Gamma[1 + \[Nu] - s] Gamma[-\[Nu] - s])/ Gamma[1 - s]) PolyGamma[1 - s])/((z - 1)/2)^s, {s, \[Gamma] - I Infinity, \[Gamma] + I Infinity}] /; \[Gamma] > 0 && \[Gamma] < -Re[\[Nu]] && \[Gamma] < 1 + Re[\[Nu]]








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