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 ArcSech

 http://functions.wolfram.com/01.30.27.0691.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-08-21