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 ArcCoth

 http://functions.wolfram.com/01.28.27.3392.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-09-04