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variants of this functions
LegendreP






Mathematica Notation

Traditional Notation









Hypergeometric Functions > LegendreP[nu,mu,3,z] > Series representations > Generalized power series > Expansions at z==infinity





http://functions.wolfram.com/07.09.06.0037.01









  


  










Input Form





LegendreP[\[Nu], \[Mu], 3, z] == ((2^\[Nu] Gamma[1/2 + \[Nu]])/(Sqrt[Pi] Gamma[1 - \[Mu] + \[Nu]])) (z - 1)^(\[Nu] - \[Mu]/2) (z + 1)^(\[Mu]/2) Sum[((Pochhammer[\[Mu] - \[Nu], k] Pochhammer[-\[Nu], k])/ (k! Pochhammer[-2 \[Nu], k])) (2/(1 - z))^k, {k, 0, \[Nu] - \[Mu]}] - (((-1)^(\[Nu] - \[Mu]) 2^(\[Nu] + 1) Gamma[\[Mu] + \[Nu] + 1])/ (Gamma[-\[Nu]] Gamma[2 \[Nu] + 2])) (z - 1)^(-\[Mu]/2 - \[Nu] - 1) (z + 1)^(\[Mu]/2) Hypergeometric2F1[\[Nu] + 1, \[Mu] + \[Nu] + 1, 2 \[Nu] + 2, 2/(1 - z)] /; Element[2 \[Nu] + 1, Integers] && 2 \[Nu] + 1 >= 0 && Element[\[Nu] - \[Mu], Integers] && -\[Nu] <= \[Mu] <= \[Nu] + 1










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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