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 ArcTanh

 http://functions.wolfram.com/01.27.27.2965.01

 Input Form

 ArcTanh[Sqrt[z + 1]/Sqrt[z]] == (-((Pi Sqrt[z])/2)) Sqrt[-(1/z)] + ArcCsch[1/Sqrt[z]]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["ArcTanh", "[", FractionBox[SqrtBox[RowBox[List["z", "+", "1"]]], SqrtBox["z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List[RowBox[List["-", FractionBox[RowBox[List["\[Pi]", " ", SqrtBox["z"]]], RowBox[List["2", " "]]]]], SqrtBox[RowBox[List["-", FractionBox["1", "z"]]]]]], "+", RowBox[List["ArcCsch", "[", FractionBox["1", SqrtBox["z"]], "]"]]]]]]]]

 MathML Form

 tanh - 1 ( z + 1 z ) csch - 1 ( 1 z ) - π z 2 - 1 z z 1 1 2 z 1 2 -1 1 z 1 2 -1 -1 z 1 2 2 -1 -1 1 z -1 1 2 [/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["1", "2"], " ", RowBox[List["(", RowBox[List["-", RowBox[List["(", RowBox[List["\[Pi]", " ", SqrtBox["z"]]], ")"]]]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox["1", "z"]]]]]], "+", RowBox[List["ArcCsch", "[", FractionBox["1", SqrtBox["z"]], "]"]]]]]]]]

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

 2003-08-21