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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/05.08.06.0032.01









  


  








Input Form





LaguerreL[n, \[Lambda], z] \[Proportional] ((Gamma[n + \[Lambda] + 1]/n!) E^(z/2) Sum[Subscript[A, k] (z/(2 (2 n + \[Lambda] + 1)))^(k/2) BesselJ[\[Lambda] + k, Sqrt[2 (2 n + \[Lambda] + 1) z]], {k, 0, Infinity}])/(((2 n + \[Lambda] + 1)/2)^(\[Lambda]/2) z^(\[Lambda]/2)) /; (n -> Infinity) && Subscript[A, 0] == 1 && Subscript[A, 1] == 0 && Subscript[A, 2] == (\[Lambda] + 1)/2 && Subscript[A, m] == ((m + \[Lambda] - 1)/m) Subscript[A, m - 2] - (2 n + \[Lambda] + 1) Subscript[A, m - 3] && Element[m, Integers] && m > 0








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