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 ArcSin

 http://functions.wolfram.com/01.12.27.1327.01

 Input Form

 ArcSin[Sqrt[(z - 1)/z]] == (Sqrt[z - 1]/Sqrt[1 - z]) ArcCosh[Sqrt[1/z]] /; Abs[Arg[z]] < Pi

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcSin", "[", SqrtBox[FractionBox[RowBox[List["z", "-", "1"]], "z"]], "]"]], "\[Equal]", " ", RowBox[List[FractionBox[SqrtBox[RowBox[List["z", "-", "1"]]], SqrtBox[RowBox[List["1", "-", "z"]]]], " ", RowBox[List["ArcCosh", "[", SqrtBox[FractionBox["1", "z"]], "]"]]]]]], "/;", RowBox[List[RowBox[List["Abs", "[", RowBox[List["Arg", "[", "z", "]"]], "]"]], "<", "\[Pi]"]]]]]]

 MathML Form

 sin - 1 ( z - 1 z ) z - 1 1 - z cosh - 1 ( 1 z ) /; "\[LeftBracketingBar]" arg ( z ) "\[RightBracketingBar]" < π Condition z -1 z -1 1 2 z -1 1 2 1 -1 z 1 2 -1 1 z -1 1 2 z [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcSin", "[", SqrtBox[FractionBox[RowBox[List["z_", "-", "1"]], "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[SqrtBox[RowBox[List["z", "-", "1"]]], " ", RowBox[List["ArcCosh", "[", SqrtBox[FractionBox["1", "z"]], "]"]]]], SqrtBox[RowBox[List["1", "-", "z"]]]], "/;", RowBox[List[RowBox[List["Abs", "[", RowBox[List["Arg", "[", "z", "]"]], "]"]], "<", "\[Pi]"]]]]]]]]

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

 2003-08-21