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 ArcCot

 http://functions.wolfram.com/01.16.07.0001.01

 Input Form

 ArcCot[z] == z Integrate[1/(z^2 t^2 + 1), {t, 1, Infinity}] /; Re[z] > 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcCot", "[", "z", "]"]], "\[Equal]", RowBox[List["z", RowBox[List[SubsuperscriptBox["\[Integral]", "1", "\[Infinity]"], RowBox[List[FractionBox["1", RowBox[List[RowBox[List[SuperscriptBox["z", "2"], SuperscriptBox["t", "2"]]], "+", "1"]]], " ", RowBox[List["\[DifferentialD]", "t"]]]]]]]]]], "/;", RowBox[List[RowBox[List["Re", "[", "z", "]"]], ">", "0"]]]]]]

 MathML Form

 cot - 1 ( z ) z 1 1 z 2 t 2 + 1 t /; Re ( z ) > 0 Condition z z t 1 1 z 2 t 2 1 -1 z 0 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCot", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["z", " ", RowBox[List[SubsuperscriptBox["\[Integral]", "1", "\[Infinity]"], RowBox[List[FractionBox["1", RowBox[List[RowBox[List[SuperscriptBox["z", "2"], " ", SuperscriptBox["t", "2"]]], "+", "1"]]], RowBox[List["\[DifferentialD]", "t"]]]]]]]], "/;", RowBox[List[RowBox[List["Re", "[", "z", "]"]], ">", "0"]]]]]]]]

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

 2001-10-29