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 ArcCoth

 http://functions.wolfram.com/01.28.27.2020.01

 Input Form

 ArcCoth[Sqrt[z]] == (1/2) ArcSinh[(I (1 + z))/(1 - z)] + (Pi I)/4 /; Im[z] < 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcCoth", "[", SqrtBox["z"], "]"]], "\[Equal]", RowBox[List[RowBox[List[FractionBox["1", "2"], RowBox[List["ArcSinh", "[", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]]]], RowBox[List["1", "-", "z"]]], "]"]]]], "+", FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "4"]]]]], "/;", RowBox[List[RowBox[List["Im", "[", "z", "]"]], "<", "0"]]]]]]

 MathML Form

 coth - 1 ( z ) 1 2 sinh - 1 ( ( 1 + z ) 1 - z ) + π 4 /; Im ( z ) < 0 Condition z 1 2 1 2 1 z 1 -1 z -1 4 -1 z 0 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCoth", "[", SqrtBox["z_"], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["ArcSinh", "[", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]]]], RowBox[List["1", "-", "z"]]], "]"]]]], "+", FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "4"]]], "/;", RowBox[List[RowBox[List["Im", "[", "z", "]"]], "<", "0"]]]]]]]]

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

 2003-09-04