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 LaguerreL

 http://functions.wolfram.com/05.02.21.0008.01

 Input Form

 Integrate[(LaguerreL[m, t] LaguerreL[n, t])/E^t, {t, 0, Infinity}] == KroneckerDelta[n, m]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[SubsuperscriptBox["\[Integral]", "0", "\[Infinity]"], RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", "t"]]], " ", RowBox[List["LaguerreL", "[", RowBox[List["m", ",", "t"]], "]"]], " ", RowBox[List["LaguerreL", "[", RowBox[List["n", ",", "t"]], "]"]], RowBox[List["\[DifferentialD]", "t"]]]]]], "\[Equal]", RowBox[List["KroneckerDelta", "[", RowBox[List["n", ",", "m"]], "]"]]]]]]

 MathML Form

 0 - t L m ( t ) L n ( t ) t δ KroneckerDelta n , m t 0 -1 t LaguerreL m t LaguerreL n t KroneckerDelta n m [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubsuperscriptBox["\[Integral]", "0", "\[Infinity]"], RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", "t_"]]], " ", RowBox[List["LaguerreL", "[", RowBox[List["m_", ",", "t_"]], "]"]], " ", RowBox[List["LaguerreL", "[", RowBox[List["n_", ",", "t_"]], "]"]]]], RowBox[List["\[DifferentialD]", "t_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List["KroneckerDelta", "[", RowBox[List["n", ",", "m"]], "]"]]]]]]

 Date Added to functions.wolfram.com (modification date)

 2001-10-29

© 1998-2013 Wolfram Research, Inc.