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 ArcTanh

 http://functions.wolfram.com/01.27.27.2210.01

 Input Form

 ArcTanh[Sqrt[z^2 + 1]/Sqrt[z^2]] == (Pi I)/2 + ArcSinh[z] /; -(Pi/2) < Arg[z] < 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcTanh", "[", FractionBox[SqrtBox[RowBox[List[SuperscriptBox["z", "2"], "+", "1"]]], SqrtBox[SuperscriptBox["z", "2"]]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "2"], "+", RowBox[List["ArcSinh", "[", "z", "]"]]]]]], "/;", RowBox[List[RowBox[List["-", FractionBox["\[Pi]", "2"]]], "<", RowBox[List["Arg", "[", "z", "]"]], "<", "0"]]]]]]

 MathML Form

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

 Rule Form

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

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

 2003-08-21