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 ArcCoth

 http://functions.wolfram.com/01.28.27.2413.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCoth", "[", SqrtBox["z_"], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", RowBox[List["(", RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], ")"]]]], "+", RowBox[List["ArcCosh", "[", SqrtBox[FractionBox["1", RowBox[List["1", "-", "z"]]]], "]"]]]], "/;", RowBox[List[RowBox[List["Im", "[", "z", "]"]], "\[GreaterEqual]", "0"]]]]]]]]

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

 2003-09-04