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variants of this functions
LegendreQ






Mathematica Notation

Traditional Notation









Hypergeometric Functions > LegendreQ[nu,z] > Series representations > Generalized power series > Expansions at z==infinity





http://functions.wolfram.com/07.10.06.0017.01









  


  










Input Form





LegendreQ[\[Nu], z] == (2^(-\[Nu] - 2)/Sqrt[Pi]) (z - 1)^(-\[Nu] - 1) (((2^(2 \[Nu] + 1) Gamma[1/2 + \[Nu]])/Gamma[1 + \[Nu]]) (z - 1)^(2 \[Nu] + 1) (Log[1 + z] - Log[-z - 1]) Sum[(Pochhammer[-\[Nu], k]^2/(k! Pochhammer[-2 \[Nu], k])) (2/(1 - z))^k, {k, 0, Infinity}] + (Gamma[-(1/2) - \[Nu]]/Gamma[-\[Nu]]) (2 Pi Cot[Pi \[Nu]] + Log[1 + z] - Log[-z - 1]) Sum[(Pochhammer[\[Nu] + 1, k]^2/ (k! Pochhammer[2 \[Nu] + 2, k])) (2/(1 - z))^k, {k, 0, Infinity}]) /; Abs[1 - z] > 2 && !Element[\[Nu], Integers]










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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