html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 ArcCoth

 http://functions.wolfram.com/01.28.16.0220.01

 Input Form

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

 Standard Form

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"+", FractionBox["\[ImaginaryI]", "x"]]], SqrtBox[RowBox[List["1", "-", FractionBox["1", SuperscriptBox["x", "2"]]]]]], "]"]], "+", RowBox[List["Arg", "[", RowBox[List[SqrtBox[RowBox[List["1", "-", FractionBox["1", SuperscriptBox["y", "2"]]]]], "+", FractionBox["\[ImaginaryI]", "y"]]], "]"]]]], RowBox[List["2", " ", "\[Pi]"]]]]], "]"]]]], "-", "1"]], ")"]]]], "+", RowBox[List[FractionBox["1", "2"], " ", "\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List[RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[RowBox[List["Arg", "[", FractionBox[RowBox[List[FractionBox["1", "y"], "-", FractionBox[RowBox[List[SqrtBox[RowBox[List[FractionBox["1", "y"], "-", "1"]]], " ", SqrtBox[RowBox[List["1", "+", FractionBox["1", "y"]]]]]], "x"]]], SqrtBox[RowBox[List["1", "-", FractionBox["1", SuperscriptBox["x", "2"]]]]]], "]"]], "\[Pi]"]]], "]"]], "+", RowBox[List["Floor", "[", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["Arg", "[", RowBox[List["1", "-", FractionBox["1", SuperscriptBox["x", "2"]]]], "]"]], RowBox[List["2", " ", "\[Pi]"]]]]], "+", FractionBox[RowBox[List["Arg", "[", RowBox[List[RowBox[List["\[ImaginaryI]", " ", SqrtBox[RowBox[List[FractionBox["1", "y"], "-", "1"]]], " ", SqrtBox[RowBox[List["1", "+", FractionBox["1", "y"]]]]]], "-", FractionBox["\[ImaginaryI]", RowBox[List["x", " ", "y"]]]]], "]"]], "\[Pi]"], "+", FractionBox["1", "2"]]], "]"]]]]], " ", "\[Pi]"]]]]]]]]

 MathML Form

 coth - 1 ( x ) - sech - 1 ( y ) coth - 1 ( ( - 1 ) 1 2 - arg ( 1 y - 1 y - 1 1 + 1 y x 1 - 1 x 2 ) π ( 1 x y - 1 y - 1 1 + 1 y ) 1 - 1 x 2 ( 1 y - 1 1 + 1 y - 1 x y ) 2 1 - 1 x 2 + 1 ) - 1 4 ( 1 - ( - 1 ) - - arg ( 1 - 1 y ) 2 π ) π ( 2 ( 1 + ( - 1 ) 1 2 - arg ( 1 - 1 y 2 x + 1 y 1 - 1 x 2 ) π ) arg ( - x 1 - 1 x 2 ) + arg ( 1 - 1 y 2 + y ) 2 π + ( - 1 ) 1 2 - arg ( 1 - 1 y 2 x + 1 y 1 - 1 x 2 ) π - 2 ( - 1 + ( - 1 ) 1 2 - arg ( 1 - 1 y 2 x + 1 y 1 - 1 x 2 ) π ) 1 2 - arg ( - x 1 - 1 x 2 ) + arg ( 1 - 1 y 2 + y ) 2 π - 1 ) + 1 4 ( 1 + ( - 1 ) - - arg ( 1 - 1 y ) 2 π ) π ( 2 ( 1 + ( - 1 ) 1 2 - arg ( 1 y - 1 - 1 y 2 x 1 - 1 x 2 ) π ) arg ( + x 1 - 1 x 2 ) + arg ( 1 - 1 y 2 + y ) 2 π + ( - 1 ) 1 2 - arg ( 1 y - 1 - 1 y 2 x 1 - 1 x 2 ) π - 2 ( - 1 + ( - 1 ) 1 2 - arg ( 1 y - 1 - 1 y 2 x 1 - 1 x 2 ) π ) 1 2 - arg ( + x 1 - 1 x 2 ) + arg ( 1 - 1 y 2 + y ) 2 π - 1 ) + 1 2 ( - 1 ) - arg ( 1 - 1 x 2 ) 2 π + arg ( 1 y - 1 1 + 1 y - x y ) π + 1 2 + 1 2 - arg ( 1 y - 1 y - 1 1 + 1 y x 1 - 1 x 2 ) π π x -1 y -1 1 2 -1 1 y -1 -1 1 y -1 -1 1 2 1 1 y -1 1 2 x -1 1 -1 1 x 2 -1 1 2 -1 -1 1 x y -1 -1 1 y -1 -1 1 2 1 1 y -1 1 2 1 -1 1 x 2 -1 1 2 1 y -1 -1 1 2 1 1 y -1 1 2 -1 1 x y -1 2 1 -1 1 x 2 -1 -1 1 1 2 -1 -1 1 4 1 -1 -1 -1 -1 1 -1 1 y -1 2 -1 2 1 -1 1 2 -1 1 -1 1 y 2 -1 1 2 x -1 1 y -1 1 -1 1 x 2 -1 1 2 -1 -1 -1 x -1 1 -1 1 x 2 -1 1 2 -1 1 -1 1 y 2 -1 1 2 y -1 2 -1 -1 1 2 -1 1 -1 1 y 2 -1 1 2 x -1 1 y -1 1 -1 1 x 2 -1 1 2 -1 -1 -1 2 -1 -1 1 2 -1 1 -1 1 y 2 -1 1 2 x -1 1 y -1 1 -1 1 x 2 -1 1 2 -1 -1 1 2 -1 -1 x -1 1 -1 1 x 2 -1 1 2 -1 1 -1 1 y 2 -1 1 2 y -1 2 -1 -1 1 4 1 -1 -1 -1 1 -1 1 y -1 2 -1 2 1 -1 1 2 -1 1 y -1 -1 1 -1 1 y 2 -1 1 2 x -1 1 -1 1 x 2 -1 1 2 -1 -1 x -1 1 -1 1 x 2 -1 1 2 -1 1 -1 1 y 2 -1 1 2 y -1 2 -1 -1 1 2 -1 1 y -1 -1 1 -1 1 y 2 -1 1 2 x -1 1 -1 1 x 2 -1 1 2 -1 -1 -1 2 -1 -1 1 2 -1 1 y -1 -1 1 -1 1 y 2 -1 1 2 x -1 1 -1 1 x 2 -1 1 2 -1 -1 1 2 -1 x -1 1 -1 1 x 2 -1 1 2 -1 1 -1 1 y 2 -1 1 2 y -1 2 -1 -1 1 2 -1 -1 1 -1 1 x 2 -1 2 -1 1 y -1 -1 1 2 1 1 y -1 1 2 -1 x y -1 -1 1 2 1 2 -1 1 y -1 -1 1 y -1 -1 1 2 1 1 y -1 1 2 x -1 1 -1 1 x 2 -1 1 2 -1 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["ArcCoth", "[", "x_", "]"]], "-", RowBox[List["ArcSech", "[", "y_", "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["ArcCoth", "[", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[RowBox[List["Arg", "[", FractionBox[RowBox[List[FractionBox["1", "y"], "-", FractionBox[RowBox[List[SqrtBox[RowBox[List[FractionBox["1", "y"], "-", "1"]]], " ", SqrtBox[RowBox[List["1", "+", FractionBox["1", "y"]]]]]], "x"]]], SqrtBox[RowBox[List["1", "-", FractionBox["1", SuperscriptBox["x", "2"]]]]]], "]"]], "\[Pi]"]]], "]"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SqrtBox[RowBox[List[FractionBox["1", "y"], "-", "1"]]]]], " ", SqrtBox[RowBox[List["1", "+", FractionBox["1", "y"]]]]]], "+", FractionBox["1", RowBox[List["x", " ", "y"]]]]], ")"]]]], 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 Date Added to functions.wolfram.com (modification date)

 2007-05-02