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ArcCoth






Mathematica Notation

Traditional Notation









Elementary Functions > ArcCoth[z] > Series representations > Generalized power series > Expansions at generic point z==z0 > For the function itself





http://functions.wolfram.com/01.28.06.0019.01









  


  










Input Form





ArcCoth[z] \[Proportional] ArcCoth[Subscript[z, 0]] + (1/2) Floor[Arg[-z + Subscript[z, 0]]/(2 Pi)] (Log[(1 + Subscript[z, 0])/Subscript[z, 0]] + Log[Subscript[z, 0]/(1 + Subscript[z, 0])]) - (1/2) Floor[Arg[z - Subscript[z, 0]]/(2 Pi)] (Log[(-1 + Subscript[z, 0])/Subscript[z, 0]] + Log[Subscript[z, 0]/(-1 + Subscript[z, 0])]) + (1/(1 - Subscript[z, 0]^2)) (z - Subscript[z, 0]) + (Subscript[z, 0]/(-1 + Subscript[z, 0]^2)^2) (z - Subscript[z, 0])^2 + \[Ellipsis] /; (z -> Subscript[z, 0])










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["ArcCoth", "[", SubscriptBox["zz", "0"], "]"]], "+", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["Arg", "[", RowBox[List[RowBox[List["-", "z"]], "+", SubscriptBox["zz", "0"]]], "]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", FractionBox[RowBox[List["1", "+", SubscriptBox["zz", "0"]]], SubscriptBox["zz", "0"]], "]"]], "+", RowBox[List["Log", "[", FractionBox[SubscriptBox["zz", "0"], RowBox[List["1", "+", SubscriptBox["zz", "0"]]]], "]"]]]], ")"]]]], "-", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["Arg", "[", RowBox[List["z", "-", SubscriptBox["zz", "0"]]], "]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", FractionBox[RowBox[List[RowBox[List["-", "1"]], "+", SubscriptBox["zz", "0"]]], SubscriptBox["zz", "0"]], "]"]], "+", RowBox[List["Log", "[", FractionBox[SubscriptBox["zz", "0"], RowBox[List[RowBox[List["-", "1"]], "+", SubscriptBox["zz", "0"]]]], "]"]]]], ")"]]]], "+", FractionBox[RowBox[List["z", "-", SubscriptBox["zz", "0"]]], RowBox[List["1", "-", SubsuperscriptBox["zz", "0", "2"]]]], "+", FractionBox[RowBox[List[SubscriptBox["zz", "0"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", SubscriptBox["zz", "0"]]], ")"]], "2"]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SubsuperscriptBox["zz", "0", "2"]]], ")"]], "2"]], "+", "\[Ellipsis]"]], "/;", RowBox[List["(", RowBox[List["z", "\[Rule]", SubscriptBox["zz", "0"]]], ")"]]]]]]]]










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





2007-05-02





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