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ArcCot






Mathematica Notation

Traditional Notation









Elementary Functions > ArcCot[z] > Transformations > Products, sums, and powers of the direct function > Sums of the direct function





http://functions.wolfram.com/01.16.16.0185.01









  


  










Input Form





ArcCot[x] + ArcCot[y] == ArcCot[(x y - 1)/(x + y)] + (Pi/2) (1 - Sqrt[x^2]/x - Sqrt[y^2]/y + ((x + y)/(-1 + x y)) Sqrt[((-1 + x y)/(x + y))^2]) + Pi Floor[(Pi - 2 Arg[-1 - I x] - 2 Arg[-1 - I y] + 2 Arg[x + y])/(4 Pi)] - Pi Floor[(1/(4 Pi)) (3 Pi - 2 Arg[-1 + I x] - 2 Arg[-1 + I y] + 2 Arg[x + y])]










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["ArcCot", "[", "x_", "]"]], "+", RowBox[List["ArcCot", "[", "y_", "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["ArcCot", "[", FractionBox[RowBox[List[RowBox[List["x", " ", "y"]], "-", "1"]], RowBox[List["x", "+", "y"]]], "]"]], "+", RowBox[List[FractionBox["1", "2"], " ", "\[Pi]", " ", RowBox[List["(", RowBox[List["1", "-", FractionBox[SqrtBox[SuperscriptBox["x", "2"]], "x"], "-", FractionBox[SqrtBox[SuperscriptBox["y", "2"]], "y"], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["x", "+", "y"]], ")"]], " ", SqrtBox[SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["x", " ", "y"]]]], RowBox[List["x", "+", "y"]]], ")"]], "2"]]]], RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["x", " ", "y"]]]]]]], ")"]]]], "+", RowBox[List["\[Pi]", " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["\[Pi]", "-", RowBox[List["2", " ", RowBox[List["Arg", "[", RowBox[List[RowBox[List["-", "1"]], "-", RowBox[List["\[ImaginaryI]", " ", "x"]]]], "]"]]]], "-", RowBox[List["2", " ", RowBox[List["Arg", "[", RowBox[List[RowBox[List["-", "1"]], "-", RowBox[List["\[ImaginaryI]", " ", "y"]]]], "]"]]]], "+", RowBox[List["2", " ", RowBox[List["Arg", "[", RowBox[List["x", "+", "y"]], "]"]]]]]], RowBox[List["4", " ", "\[Pi]"]]], "]"]]]], "-", RowBox[List["\[Pi]", " ", RowBox[List["Floor", "[", FractionBox[RowBox[List[RowBox[List["3", " ", "\[Pi]"]], "-", RowBox[List["2", " ", RowBox[List["Arg", "[", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["\[ImaginaryI]", " ", "x"]]]], "]"]]]], "-", RowBox[List["2", " ", RowBox[List["Arg", "[", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["\[ImaginaryI]", " ", "y"]]]], "]"]]]], "+", RowBox[List["2", " ", RowBox[List["Arg", "[", RowBox[List["x", "+", "y"]], "]"]]]]]], RowBox[List["4", " ", "\[Pi]"]]], "]"]]]]]]]]]]










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





2007-05-02