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 ArcSech

 http://functions.wolfram.com/01.30.27.0044.02

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2001-10-29