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 ArcCosh

 http://functions.wolfram.com/01.26.27.0616.01

 Input Form

 ArcCosh[Sqrt[z/(z + 1)]] == (Pi/2) Sqrt[z] Sqrt[-(1/z)] - Sqrt[z] Sqrt[-(1/z)] ArcTan[Sqrt[z]]

 Standard Form

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

 MathML Form

 cosh - 1 ( z z + 1 ) 1 2 π z - 1 z - z - 1 z tan - 1 ( z ) z z 1 -1 1 2 1 2 z 1 2 -1 1 z -1 1 2 -1 z 1 2 -1 1 z -1 1 2 z 1 2 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCosh", "[", SqrtBox[FractionBox["z_", RowBox[List["z_", "+", "1"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", "\[Pi]", " ", SqrtBox["z"], " ", SqrtBox[RowBox[List["-", FractionBox["1", "z"]]]]]], "-", RowBox[List[SqrtBox["z"], " ", SqrtBox[RowBox[List["-", FractionBox["1", "z"]]]], " ", RowBox[List["ArcTan", "[", SqrtBox["z"], "]"]]]]]]]]]]

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

 2003-08-21