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 ArcSin

 http://functions.wolfram.com/01.12.27.1274.01

 Input Form

 ArcSin[1/Sqrt[z]] == (Pi/2) Sqrt[z] Sqrt[1/z] - (Sqrt[-1 + z]/Sqrt[1 - z]) ArcCosh[Sqrt[1/z]]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["ArcSin", "[", FractionBox["1", SqrtBox["z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List[FractionBox["\[Pi]", "2"], SqrtBox["z"], SqrtBox[FractionBox["1", "z"]]]], "-", RowBox[List[FractionBox[SqrtBox[RowBox[List[RowBox[List["-", "1"]], "+", "z"]]], SqrtBox[RowBox[List["1", "-", "z"]]]], " ", RowBox[List["ArcCosh", "[", SqrtBox[FractionBox["1", "z"]], "]"]]]]]]]]]]

 MathML Form

 sin - 1 ( 1 z ) π 2 z 1 z - z - 1 1 - z cosh - 1 ( 1 z ) 1 z 1 2 -1 2 -1 z 1 2 1 z -1 1 2 -1 z -1 1 2 1 -1 z 1 2 -1 1 z -1 1 2 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcSin", "[", FractionBox["1", SqrtBox["z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", "\[Pi]", " ", SqrtBox["z"], " ", SqrtBox[FractionBox["1", "z"]]]], "-", FractionBox[RowBox[List[SqrtBox[RowBox[List[RowBox[List["-", "1"]], "+", "z"]]], " ", RowBox[List["ArcCosh", "[", SqrtBox[FractionBox["1", "z"]], "]"]]]], SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]

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

 2003-08-21