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 Exp

 http://functions.wolfram.com/01.03.21.0031.01

 Input Form

 Integrate[t^k/E^t, {t, 0, Infinity}] == Gamma[k + 1] /; Re[k] > -1

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[SubsuperscriptBox["\[Integral]", "0", "\[Infinity]"], RowBox[List[SuperscriptBox["t", "k"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", "t"]]], RowBox[List["\[DifferentialD]", "t"]]]]]], "\[Equal]", RowBox[List["Gamma", "[", RowBox[List["k", "+", "1"]], "]"]]]], "/;", RowBox[List[RowBox[List["Re", "[", "k", "]"]], ">", RowBox[List["-", "1"]]]]]]]]

 MathML Form

 0 t k - t t Γ ( k + 1 ) /; Re ( k ) > - 1 Condition t 0 t k -1 t Gamma k 1 k -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubsuperscriptBox["\[Integral]", "0", "\[Infinity]"], RowBox[List[RowBox[List[SuperscriptBox["t_", "k_"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", "t_"]]]]], RowBox[List["\[DifferentialD]", "t_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Gamma", "[", RowBox[List["k", "+", "1"]], "]"]], "/;", RowBox[List[RowBox[List["Re", "[", "k", "]"]], ">", RowBox[List["-", "1"]]]]]]]]]]

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

 2001-10-29