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 ArcSin

 http://functions.wolfram.com/01.12.16.0025.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2001-10-29