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 ArcCoth

 http://functions.wolfram.com/01.28.27.0228.01

 Input Form

 ArcCoth[1/Sqrt[z]] == I ArcSin[Sqrt[z/(z - 1)]] /; Inequality[0, Less, Arg[z], LessEqual, Pi]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcCoth", "[", FractionBox["1", SqrtBox["z"]], "]"]], "\[Equal]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSin", "[", SqrtBox[FractionBox["z", RowBox[List["z", "-", "1"]]]], "]"]]]]]], "/;", RowBox[List["0", "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", "\[Pi]"]]]]]]

 MathML Form

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

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCoth", "[", FractionBox["1", SqrtBox["z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSin", "[", SqrtBox[FractionBox["z", RowBox[List["z", "-", "1"]]]], "]"]]]], "/;", RowBox[List["0", "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", "\[Pi]"]]]]]]]]

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

 2003-09-04