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 ArcCsc

 http://functions.wolfram.com/01.17.16.0009.01

 Input Form

 ArcCsc[z/Sqrt[z^2 - 1]] == (Pi Sqrt[z^2])/(2 z) - Sqrt[1/z^2] Sqrt[z^2] ArcCsc[z]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["ArcCsc", "[", FractionBox["z", SqrtBox[RowBox[List[SuperscriptBox["z", "2"], "-", "1"]]]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["\[Pi]", " ", SqrtBox[SuperscriptBox["z", "2"]]]], RowBox[List["2", " ", "z"]]], "-", RowBox[List[SqrtBox[FractionBox["1", SuperscriptBox["z", "2"]]], " ", SqrtBox[SuperscriptBox["z", "2"]], " ", RowBox[List["ArcCsc", "[", "z", "]"]]]]]]]]]]

 MathML Form

 csc - 1 ( z z 2 - 1 ) π z 2 2 z - 1 z 2 z 2 csc - 1 ( z ) z z 2 -1 1 2 -1 z 2 1 2 2 z -1 -1 1 z 2 -1 1 2 z 2 1 2 z [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCsc", "[", FractionBox["z_", SqrtBox[RowBox[List[SuperscriptBox["z_", "2"], "-", "1"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["\[Pi]", " ", SqrtBox[SuperscriptBox["z", "2"]]]], RowBox[List["2", " ", "z"]]], "-", RowBox[List[SqrtBox[FractionBox["1", SuperscriptBox["z", "2"]]], " ", SqrtBox[SuperscriptBox["z", "2"]], " ", RowBox[List["ArcCsc", "[", "z", "]"]]]]]]]]]]

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

 2001-10-29