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 ArcSin

 http://functions.wolfram.com/01.12.27.0154.01

 Input Form

 ArcSin[Sqrt[z + 1]] == Pi/2 - I ArcSinh[Sqrt[z]] /; Inequality[-Pi, Less, Arg[z], LessEqual, 0]

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2001-10-29