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 ArcSin

 http://functions.wolfram.com/01.12.27.0150.02

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2001-10-29