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 ArcCoth

 http://functions.wolfram.com/01.28.27.1277.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-09-04