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 ArcCot

 http://functions.wolfram.com/01.16.26.0015.01

 Input Form

 ArcCot[z] == (-I) Sqrt[-1 + z] EllipticPi[z, I ArcTanh[1/(z Sqrt[-1 + z])], 0]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["ArcCot", "[", "z", "]"]], "\[Equal]", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], SqrtBox[RowBox[List[RowBox[List["-", "1"]], "+", "z"]]], RowBox[List["EllipticPi", "[", RowBox[List["z", ",", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcTanh", "[", FractionBox["1", RowBox[List["z", SqrtBox[RowBox[List[RowBox[List["-", "1"]], "+", "z"]]]]]], "]"]]]], ",", "0"]], "]"]]]]]]]]

 MathML Form

 cot - 1 ( z ) - z - 1 Π ( z ; tanh - 1 ( 1 z z - 1 ) 0 ) z -1 z -1 1 2 EllipticPi z 1 z z -1 1 2 -1 0 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCot", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", SqrtBox[RowBox[List[RowBox[List["-", "1"]], "+", "z"]]], " ", RowBox[List["EllipticPi", "[", RowBox[List["z", ",", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcTanh", "[", FractionBox["1", RowBox[List["z", " ", SqrtBox[RowBox[List[RowBox[List["-", "1"]], "+", "z"]]]]]], "]"]]]], ",", "0"]], "]"]]]]]]]]

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

 2001-10-29

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