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 ArcTanh

 http://functions.wolfram.com/01.27.27.1315.01

 Input Form

 ArcTanh[1/Sqrt[z]] == I ArcCsc[Sqrt[z - 1]/Sqrt[z]] - (Pi I)/2 /; Im[z] >= 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcTanh", "[", FractionBox["1", SqrtBox["z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcCsc", "[", FractionBox[SqrtBox[RowBox[List["z", "-", "1"]]], SqrtBox["z"]], "]"]]]], "-", FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "2"]]]]], "/;", RowBox[List[RowBox[List["Im", "[", "z", "]"]], "\[GreaterEqual]", "0"]]]]]]

 MathML Form

 tanh - 1 ( 1 z ) csc - 1 ( z - 1 z ) - π 2 /; Im ( z ) 0 Condition 1 z 1 2 -1 z -1 1 2 z 1 2 -1 -1 2 -1 z 0 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcTanh", "[", FractionBox["1", SqrtBox["z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcCsc", "[", FractionBox[SqrtBox[RowBox[List["z", "-", "1"]]], SqrtBox["z"]], "]"]]]], "-", FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "2"]]], "/;", RowBox[List[RowBox[List["Im", "[", "z", "]"]], "\[GreaterEqual]", "0"]]]]]]]]

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

 2003-08-21