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 LaguerreL

 http://functions.wolfram.com/05.08.06.0003.01

 Input Form

 LaguerreL[n, \[Lambda], z] == (Gamma[\[Lambda] + n + 1]/n!) Hypergeometric1F1Regularized[-n, \[Lambda] + 1, z]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["LaguerreL", "[", RowBox[List["n", ",", "\[Lambda]", ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["Gamma", "[", RowBox[List["\[Lambda]", "+", "n", "+", "1"]], "]"]], RowBox[List["n", "!"]]], " ", RowBox[List["Hypergeometric1F1Regularized", "[", RowBox[List[RowBox[List["-", "n"]], ",", RowBox[List["\[Lambda]", "+", "1"]], ",", "z"]], "]"]]]]]]]]

 MathML Form

 L n λ ( z ) Γ ( n + λ + 1 ) n ! 1 F ~ 1 ( - n ; λ + 1 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["1", TraditionalForm]], SubscriptBox[OverscriptBox["F", "~"], FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[TagBox[RowBox[List["-", "n"]], Hypergeometric1F1Regularized, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric1F1Regularized, Rule[Editable, False]], ";", TagBox[TagBox[TagBox[RowBox[List["\[Lambda]", "+", "1"]], Hypergeometric1F1Regularized, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric1F1Regularized, Rule[Editable, False]], ";", TagBox["z", Hypergeometric1F1Regularized, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQRegularized[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], Hypergeometric1F1Regularized] LaguerreL n λ z Gamma n λ 1 n -1 Hypergeometric1F1Regularized -1 n λ 1 z [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LaguerreL", "[", RowBox[List["n_", ",", "\[Lambda]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["Gamma", "[", RowBox[List["\[Lambda]", "+", "n", "+", "1"]], "]"]], " ", RowBox[List["Hypergeometric1F1Regularized", "[", RowBox[List[RowBox[List["-", "n"]], ",", RowBox[List["\[Lambda]", "+", "1"]], ",", "z"]], "]"]]]], RowBox[List["n", "!"]]]]]]]

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

 2001-10-29