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variants of this functions
LaguerreL






Mathematica Notation

Traditional Notation









Polynomials > LaguerreL[n,lambda,z] > Integration > Definite integration > Involving the direct function





http://functions.wolfram.com/05.08.21.0009.01









  


  










Input Form





Integrate[(t^(\[Alpha] - 1) LaguerreL[m, \[Lambda], a t] LaguerreL[n, \[Beta], b t])/E^(p t), {t, 0, Infinity}] == ((Gamma[\[Alpha]] Pochhammer[\[Lambda] + 1, m] Pochhammer[\[Beta] + 1, n])/ (p^\[Alpha] (m! n!))) Sum[((Pochhammer[-m, j] Pochhammer[\[Alpha], j])/ (Pochhammer[\[Lambda] + 1, j] j!)) (a/p)^j Sum[((Pochhammer[-n, k] Pochhammer[\[Alpha] + j, k])/ (Pochhammer[\[Beta] + 1, k] k!)) (b/p)^k, {k, 0, n}], {j, 0, m}] /; Re[\[Alpha]] > 0 && Re[p] > 0 && Element[m, Integers] && m >= 0 && 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





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