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 ArcSech

 http://functions.wolfram.com/01.30.27.2260.01

 Input Form

 ArcSech[z] == 2 Pi I + 2 ArcCoth[Sqrt[1 + z]/Sqrt[1 - z]] /; Element[z, Reals] && -1 < z < 0

 Standard Form

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

 MathML Form

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

 Rule Form

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