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 ArcCosh

 http://functions.wolfram.com/01.26.27.2205.01

 Input Form

 ArcCosh[Sqrt[-z]] == -ArcCsch[1/Sqrt[z]] + (Pi I)/2 /; Element[z, Reals] && -1 < z < 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcCosh", "[", SqrtBox[RowBox[List["-", "z"]]], "]"]], "\[Equal]", RowBox[List[RowBox[List["-", RowBox[List["ArcCsch", "[", FractionBox["1", SqrtBox["z"]], "]"]]]], "+", FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "2"]]]]], "/;", RowBox[List["(", RowBox[List[RowBox[List["z", "\[Element]", "Reals"]], "\[And]", RowBox[List[RowBox[List["-", "1"]], "<", "z", "<", "0"]]]], ")"]]]]]]

 MathML Form

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

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCosh", "[", SqrtBox[RowBox[List["-", "z_"]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["-", RowBox[List["ArcCsch", "[", FractionBox["1", SqrtBox["z"]], "]"]]]], "+", FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "2"]]], "/;", RowBox[List[RowBox[List["z", "\[Element]", "Reals"]], "&&", RowBox[List[RowBox[List["-", "1"]], "<", "z", "<", "0"]]]]]]]]]]

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

 2003-08-21