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 Exp

 http://functions.wolfram.com/01.03.21.0034.01

 Input Form

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

 Standard Form

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

 MathML Form

 0 t k t - 1 t Γ ( k + 1 ) ζ ( k + 1 ) TagBox[RowBox[List["\[Zeta]", "(", TagBox[RowBox[List["k", "+", "1"]], Rule[Editable, True]], ")"]], InterpretTemplate[Function[Zeta[Slot[1]]]]] /; Re ( k ) > 0 Condition t 0 t k t -1 -1 Gamma k 1 Zeta k 1 k 0 [/itex]

 Rule Form

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

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

 2001-10-29