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 ArcCsch

 http://functions.wolfram.com/01.29.27.1106.01

 Input Form

 ArcCsch[1/Sqrt[z]] == (Pi I)/2 - I ArcSec[Sqrt[-(1/z)]] /; Im[z] >= 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcCsch", "[", FractionBox["1", SqrtBox["z"]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "2"], "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSec", "[", SqrtBox[RowBox[List["-", FractionBox["1", "z"]]]], "]"]]]]]]]], "/;", RowBox[List[RowBox[List["Im", "[", "z", "]"]], "\[GreaterEqual]", "0"]]]]]]

 MathML Form

 csch - 1 ( 1 z ) π 2 - sec - 1 ( - 1 z ) /; Im ( z ) 0 Condition 1 z 1 2 -1 2 -1 -1 -1 1 z -1 1 2 z 0 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCsch", "[", FractionBox["1", SqrtBox["z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "2"], "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSec", "[", SqrtBox[RowBox[List["-", FractionBox["1", "z"]]]], "]"]]]]]], "/;", RowBox[List[RowBox[List["Im", "[", "z", "]"]], "\[GreaterEqual]", "0"]]]]]]]]

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

 2003-08-21