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 ArcSin

 http://functions.wolfram.com/01.12.27.0911.01

 Input Form

 ArcSin[Sqrt[z^2/(z^2 + 1)]] == Pi + ArcCot[1/z] /; Element[I z, Reals] && I z > 1

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcSin", "[", SqrtBox[FractionBox[SuperscriptBox["z", "2"], RowBox[List[SuperscriptBox["z", "2"], "+", "1"]]]], "]"]], "\[Equal]", RowBox[List["\[Pi]", "+", RowBox[List["ArcCot", "[", FractionBox["1", "z"], "]"]]]]]], "/;", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "z"]], "\[Element]", "Reals"]], "\[And]", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "z"]], ">", "1"]]]], ")"]]]]]]

 MathML Form

 sin - 1 ( z 2 z 2 + 1 ) π + cot - 1 ( 1 z ) /; ( z z > 1 ) Condition z 2 z 2 1 -1 1 2 1 z -1 z z 1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcSin", "[", SqrtBox[FractionBox[SuperscriptBox["z_", "2"], RowBox[List[SuperscriptBox["z_", "2"], "+", "1"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["\[Pi]", "+", RowBox[List["ArcCot", "[", FractionBox["1", "z"], "]"]]]], "/;", RowBox[List[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "z"]], "\[Element]", "Reals"]], "&&", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "z"]], ">", "1"]]]]]]]]]]

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

 2003-08-21