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 ArcSech

 http://functions.wolfram.com/01.30.27.0625.01

 Input Form

 ArcSech[(1 - z)/(1 + z)] == Pi I - 2 I ArcTan[Sqrt[-(1/z)]] /; Im[z] <= 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcSech", "[", FractionBox[RowBox[List["1", "-", "z"]], RowBox[List["1", "+", "z"]]], "]"]], "\[Equal]", RowBox[List[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "-", RowBox[List["2", "\[ImaginaryI]", " ", RowBox[List["ArcTan", "[", SqrtBox[RowBox[List["-", FractionBox["1", "z"]]]], "]"]]]]]]]], "/;", RowBox[List[RowBox[List["Im", "[", "z", "]"]], "\[LessEqual]", "0"]]]]]]

 MathML Form

 sech - 1 ( 1 - z 1 + z ) π - 2 tan - 1 ( - 1 z ) /; Im ( z ) 0 Condition 1 -1 z 1 z -1 -1 2 -1 1 z -1 1 2 z 0 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcSech", "[", FractionBox[RowBox[List["1", "-", "z_"]], RowBox[List["1", "+", "z_"]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", RowBox[List["ArcTan", "[", SqrtBox[RowBox[List["-", FractionBox["1", "z"]]]], "]"]]]]]], "/;", RowBox[List[RowBox[List["Im", "[", "z", "]"]], "\[LessEqual]", "0"]]]]]]]]

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

 2003-08-21