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variants of this functions
LaguerreL




Mathematica Notation

Traditional Notation









Hypergeometric Functions > LaguerreL[nu,lambda,z] > Operations > Orthogonality, completeness, and Fourier expansions





http://functions.wolfram.com/07.03.25.0006.01









  


  








Input Form





f[x] == Sum[Subscript[c, n] Subscript[\[Psi], n][x], {n, 0, Infinity}] /; Subscript[c, n] == Integrate[Subscript[\[Psi], n][t] f[t], {t, 0, Infinity}] && Subscript[\[Psi], n][x] == Sqrt[n!/Gamma[\[Lambda] + n + 1]] x^(\[Lambda]/2) Exp[-(x/2)] LaguerreL[n, \[Lambda], x] /; Re[\[Lambda]] > -1 && x > 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)





2001-10-29