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ArcCoth






Mathematica Notation

Traditional Notation









Elementary Functions > ArcCoth[z] > Representations through more general functions > Through hypergeometric functions > Involving 2F1





http://functions.wolfram.com/01.28.26.0002.01









  


  










Input Form





ArcCoth[z] == (-(Pi/2)) Sqrt[-(1/z^2)] z + z Hypergeometric2F1[1/2, 1, 3/2, z^2] /; !IntervalMemberQ[Interval[{-Infinity, -1}], z] && !IntervalMemberQ[Interval[{1, Infinity}], z]










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCoth", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["-", "\[Pi]"]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox["1", SuperscriptBox["z", "2"]]]]], " ", "z"]], "+", RowBox[List["z", " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["1", "2"], ",", "1", ",", FractionBox["3", "2"], ",", SuperscriptBox["z", "2"]]], "]"]]]]]], "/;", RowBox[List[RowBox[List["!", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "\[Infinity]"]], ",", RowBox[List["-", "1"]]]], "}"]], "]"]], ",", "z"]], "]"]]]], "&&", RowBox[List["!", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List["1", ",", "\[Infinity]"]], "}"]], "]"]], ",", "z"]], "]"]]]]]]]]]]]]










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





2001-10-29





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