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 ArcCoth

 http://functions.wolfram.com/01.28.27.3406.01

 Input Form

 ArcCoth[Sqrt[z]/Sqrt[z - 1]] == ArcSech[1/Sqrt[z]] - Pi I /; Element[z, Reals] && z < 0

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-09-04