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variants of this functions
LaguerreL




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/05.02.06.0020.01









  


  








Input Form





LaguerreL[n, z] \[Proportional] (E^(z/2)/(Sqrt[Pi] z^(1/4) n^(1/4))) (Cos[Pi/4 - 2 Sqrt[(n + 1/2) z]] - (1/(16 Sqrt[z] Sqrt[n])) Sin[Pi/4 - 2 Sqrt[(n + 1/2) z]] - ((9 + 64 z + 64 z^2)/(512 z n)) Cos[Pi/4 - 2 Sqrt[(n + 1/2) z]] - (1/(8192 z^(3/2) n^(3/2))) (1024 (1 + 2 n) z^3 Cos[Pi/4 + 2 Sqrt[(n + 1/2) z]] + 3 (-25 + 64 z (-1 + 5 z)) Sin[Pi/4 - 2 Sqrt[(n + 1/2) z]]) + \[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