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 ArcTanh

 http://functions.wolfram.com/01.27.27.2964.01

 Input Form

 ArcTanh[Sqrt[z + 1]/Sqrt[z]] == (Pi I)/2 + ArcCsch[1/Sqrt[z]] /; Im[z] < 0

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-08-21