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variants of this functions
LaguerreL






Mathematica Notation

Traditional Notation









Polynomials > LaguerreL[n,lambda,z] > Series representations > Generalized power series > Expansions at n==infinity





http://functions.wolfram.com/05.08.06.0029.01









  


  










Input Form





LaguerreL[n, \[Lambda], z] \[Proportional] ((E^(z/2) n^((2 \[Lambda] - 1)/4))/(z^((2 \[Lambda] + 1)/4) Sqrt[Pi])) (Cos[2 Sqrt[z (n + (\[Lambda] + 1)/2)] - Pi ((2 \[Lambda] + 1)/4)] + ((1 - 4 \[Lambda]^2)/(16 Sqrt[n] Sqrt[z])) Sin[2 Sqrt[z (n + (\[Lambda] + 1)/2)] - Pi ((2 \[Lambda] + 1)/4)] + (1/(512 n z)) ((-1 + 2 \[Lambda]) (9 + 18 \[Lambda] - 4 \[Lambda]^2 - 8 \[Lambda]^3 + 64 z (1 + \[Lambda])) Cos[2 Sqrt[z (n + (\[Lambda] + 1)/2)] - Pi ((2 \[Lambda] + 1)/4)] + 64 z^2 (1 + \[Lambda]) Cos[2 Sqrt[z (n + (\[Lambda] + 1)/2)] - Pi ((2 \[Lambda] + 5)/4)]) - (1/(24576 n^(3/2) z^(3/2))) (3072 z^3 (1 + 2 n + \[Lambda]) Cos[2 Sqrt[z (n + (\[Lambda] + 1)/2)] - Pi ((2 \[Lambda] + 7)/4)] + (3 - 2 \[Lambda] - 12 \[Lambda]^2 + 8 \[Lambda]^3) (75 + 50 \[Lambda] - 12 \[Lambda]^2 - 8 \[Lambda]^3 + 192 z (1 + \[Lambda])) Sin[2 Sqrt[z (n + (\[Lambda] + 1)/2)] - Pi ((2 \[Lambda] + 1)/4)] + 192 z^2 (15 + 31 \[Lambda] + 20 \[Lambda]^2 + 4 \[Lambda]^3) Sin[2 Sqrt[z (n + (\[Lambda] + 1)/2)] - Pi ((2 \[Lambda] + 5)/4)]) + \[Ellipsis]) /; (n -> Infinity)










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)





2007-05-02





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