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 Coth

 http://functions.wolfram.com/01.22.21.0011.01

 Input Form

 Integrate[(t^2 Coth[t])/E^t, {t, 0, Infinity}] == (7 Zeta[3])/2 - 2

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[SubsuperscriptBox["\[Integral]", "0", "\[Infinity]"], RowBox[List[SuperscriptBox["t", "2"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", "t"]]], " ", RowBox[List["Coth", "[", "t", "]"]], RowBox[List["\[DifferentialD]", "t"]]]]]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["7", " ", RowBox[List["Zeta", "[", "3", "]"]]]], "2"], "-", "2"]]]]]]

 MathML Form

 0 t 2 - t coth ( t ) t 7 ζ ( 3 ) TagBox[RowBox[List["\[Zeta]", "(", TagBox["3", Rule[Editable, True]], ")"]], InterpretTemplate[Function[Zeta[Slot[1]]]]] 2 - 2 t 0 t 2 -1 t t 7 Zeta 3 2 -1 -2 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubsuperscriptBox["\[Integral]", "0", "\[Infinity]"], RowBox[List[RowBox[List[SuperscriptBox["t_", "2"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", "t_"]]], " ", RowBox[List["Coth", "[", "t_", "]"]]]], RowBox[List["\[DifferentialD]", "t_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["7", " ", RowBox[List["Zeta", "[", "3", "]"]]]], "2"], "-", "2"]]]]]]

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

 2001-10-29

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