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variants of this functions
LaguerreL




Mathematica Notation

Traditional Notation









Hypergeometric Functions > LaguerreL[nu,lambda,z] > Series representations > Generalized power series > Expansions at generic point lambda==lambda0 > For the function itself





http://functions.wolfram.com/07.03.06.0009.01









  


  








Input Form





LaguerreL[n, \[Lambda], z] \[Proportional] ((-1)^n z^n)/n! + (1/n!) Sum[(((-1)^(j + n - s) z^s)/s!) Pochhammer[-n, s] StirlingS1[n - s, j] (1 + s + Subscript[\[Lambda], 0])^j (1 + (j/(1 + s + Subscript[\[Lambda], 0])) (\[Lambda] - Subscript[\[Lambda], 0]) + (((-1 + j) j)/(2 (1 + s + Subscript[\[Lambda], 0])^2)) (\[Lambda] - Subscript[\[Lambda], 0])^2 + O[(\[Lambda] - Subscript[\[Lambda], 0])^3]), {s, 0, n}, {j, 1, n - s}] /; Element[n, Integers] && n >= 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