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 ArcCoth

 http://functions.wolfram.com/01.28.27.3023.01

 Input Form

 ArcCoth[Sqrt[1/(1 + z)]] == -((Pi I)/2) - ArcCsch[Sqrt[z]] /; Element[z, Reals] && z < 0

 Standard Form

 Cell[BoxData[RowBox[List[" ", RowBox[List[RowBox[List[RowBox[List["ArcCoth", "[", SqrtBox[FractionBox["1", RowBox[List["1", "+", "z"]]]], "]"]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "2"]]], "-", RowBox[List["ArcCsch", "[", SqrtBox["z"], "]"]]]]]], "/;", RowBox[List["(", RowBox[List[RowBox[List["z", "\[Element]", "Reals"]], "\[And]", RowBox[List["z", "<", "0"]]]], ")"]]]]]]]]

 MathML Form

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

 Rule Form

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

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

 2003-09-04