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 ArcCoth

 http://functions.wolfram.com/01.28.27.0835.01

 Input Form

 ArcCoth[Sqrt[-z]] == (Pi I)/2 - I ArcTan[1/Sqrt[1/z]] /; Im[z] > 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcCoth", "[", SqrtBox[RowBox[List["-", "z"]]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "2"], "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcTan", "[", RowBox[List["1", "/", SqrtBox[FractionBox["1", "z"]]]], "]"]]]]]]]], "/;", RowBox[List[RowBox[List["Im", "[", "z", "]"]], ">", "0"]]]]]]

 MathML Form

 coth - 1 ( - z ) π 2 - tan - 1 ( 1 / 1 z ) /; Im ( z ) > 0 Condition -1 z 1 2 2 -1 -1 1 1 z -1 1 2 -1 z 0 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCoth", "[", SqrtBox[RowBox[List["-", "z_"]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "2"], "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcTan", "[", FractionBox["1", SqrtBox[FractionBox["1", "z"]]], "]"]]]]]], "/;", RowBox[List[RowBox[List["Im", "[", "z", "]"]], ">", "0"]]]]]]]]

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

 2003-09-04