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 ArcCoth

 http://functions.wolfram.com/01.28.27.3407.01

 Input Form

 ArcCoth[Sqrt[z]/Sqrt[z - 1]] == ArcSech[1/Sqrt[z]] + ((Pi I)/2) (Sqrt[z] Sqrt[1/z] - 1)

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["ArcCoth", "[", FractionBox[SqrtBox["z"], SqrtBox[RowBox[List["z", "-", "1"]]]], "]"]], "\[Equal]", RowBox[List[RowBox[List["ArcSech", "[", FractionBox["1", SqrtBox["z"]], "]"]], "+", RowBox[List[FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "2"], " ", RowBox[List["(", RowBox[List[RowBox[List[SqrtBox["z"], " ", SqrtBox[FractionBox["1", "z"]]]], "-", "1"]], ")"]]]]]]]]]]

 MathML Form

 coth - 1 ( z z - 1 ) sech - 1 ( 1 z ) + π 2 ( z 1 z - 1 ) z 1 2 z -1 1 2 -1 1 z 1 2 -1 2 -1 z 1 2 1 z -1 1 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCoth", "[", FractionBox[SqrtBox["z_"], SqrtBox[RowBox[List["z_", "-", "1"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["ArcSech", "[", FractionBox["1", SqrtBox["z"]], "]"]], "+", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SqrtBox["z"], " ", SqrtBox[FractionBox["1", "z"]]]], "-", "1"]], ")"]]]]]]]]]]

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

 2003-09-04