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ArcCoth




Mathematica Notation

Traditional Notation









Elementary Functions > ArcCoth[z] > Series representations > Generalized power series > Expansions at z==1 > For the function itself





http://functions.wolfram.com/01.28.06.0007.01









  


  








Input Form





ArcCoth[z] == Log[2]/2 - (1/2) Log[z - 1] + ((z - 1)/4) Hypergeometric2F1[1, 1, 2, (1 - z)/2] /; !IntervalMemberQ[Interval[{-1, 0}], 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[FractionBox[RowBox[List["Log", "[", "2", "]"]], "2"], "-", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["Log", "[", RowBox[List["z", "-", "1"]], "]"]]]], "+", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["z", "-", "1"]], ")"]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List["1", ",", "1", ",", "2", ",", FractionBox[RowBox[List["1", "-", "z"]], "2"]]], "]"]]]]]], "/;", RowBox[List["!", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "1"]], ",", "0"]], "}"]], "]"]], ",", "z"]], "]"]]]]]]]]]]


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





2001-10-29