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 ArcCosh

 http://functions.wolfram.com/01.26.06.0056.01

 Input Form

 ArcCosh[z] \[Proportional] (-I) (Pi/2 - z - z^3/6 - (3 z^5)/40 + O[z^7]) /; Im[z] < 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcCosh", "[", "z", "]"]], "\[Proportional]", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], RowBox[List["(", RowBox[List[FractionBox["\[Pi]", "2"], "-", "z", "-", FractionBox[SuperscriptBox["z", "3"], "6"], "-", FractionBox[RowBox[List["3", " ", SuperscriptBox["z", "5"]]], "40"], "+", RowBox[List["O", "[", SuperscriptBox["z", "7"], "]"]]]], ")"]]]]]], "/;", RowBox[List[RowBox[List["Im", "[", "z", "]"]], "<", "0"]]]]]]

 MathML Form

 cosh - 1 ( z ) - ( π 2 - z - z 3 6 - 3 z 5 40 + O ( z 7 ) ) /; Im ( z ) < 0 Condition Proportional z -1 2 -1 -1 z -1 z 3 6 -1 -1 3 z 5 40 -1 O z 7 z 0 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCosh", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", RowBox[List["(", RowBox[List[FractionBox["\[Pi]", "2"], "-", "z", "-", FractionBox[SuperscriptBox["z", "3"], "6"], "-", FractionBox[RowBox[List["3", " ", SuperscriptBox["z", "5"]]], "40"], "+", SuperscriptBox[RowBox[List["O", "[", "z", "]"]], "7"]]], ")"]]]], "/;", RowBox[List[RowBox[List["Im", "[", "z", "]"]], "<", "0"]]]]]]]]

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

 2007-05-02