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variants of this functions
LaguerreL




Mathematica Notation

Traditional Notation









Hypergeometric Functions > LaguerreL[nu,z] > Series representations > Generalized power series > Expansions at z==0 > For the function itself > General case





http://functions.wolfram.com/07.02.06.0017.01









  


  








Input Form





LaguerreL[\[Nu], z] == Subscript[F, Infinity][z, \[Nu]] /; Subscript[F, m][z, \[Nu]] == Sum[(Pochhammer[-\[Nu], k] z^k)/k!^2, {k, 0, m}] == LaguerreL[\[Nu], z] + ((Gamma[1 + m - \[Nu]] Gamma[1 + \[Nu]] Sin[Pi \[Nu]])/(Pi (m + 1)!^2)) z^(1 + m) HypergeometricPFQ[{1, 1 + m - \[Nu]}, {2 + m, 2 + m}, z] && 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