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 ArcSech

 http://functions.wolfram.com/01.30.27.0760.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-08-21