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 ArcSech

 http://functions.wolfram.com/01.30.27.0991.01

 Input Form

 ArcSech[Sqrt[(z + 1)/z]] == (Pi I)/2 - I ArcCot[Sqrt[1/z]] /; Inequality[0, LessEqual, Arg[z], Less, Pi]

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-08-21