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: 10px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 ArcCosh

 http://functions.wolfram.com/01.26.16.0207.01

 Input Form

 ArcCosh[x] - ArcSinh[y] == (I Sqrt[(-1)^Floor[1/2 - Arg[I Sqrt[x - 1] Sqrt[x + 1] Sqrt[y^2 + 1] - I x y]/Pi] (x Sqrt[y^2 + 1] - Sqrt[x - 1] Sqrt[x + 1] y) + 1] ArcCosh[(-1)^Floor[1/2 - Arg[I Sqrt[x - 1] Sqrt[x + 1] Sqrt[y^2 + 1] - I x y]/Pi] (Sqrt[x - 1] Sqrt[x + 1] y - x Sqrt[y^2 + 1])])/ Sqrt[(-(-1)^Floor[1/2 - Arg[I Sqrt[x - 1] Sqrt[x + 1] Sqrt[y^2 + 1] - I x y]/Pi]) (x Sqrt[y^2 + 1] - Sqrt[x - 1] Sqrt[x + 1] y) - 1] - (1/2) I Pi ((1/2) (1 - (-1)^(-Floor[-(Arg[1 - x]/(2 Pi))])) (2 (-1 + (-1)^Floor[1/2 - Arg[Sqrt[1 - x^2] Sqrt[y^2 + 1] - I x y]/Pi]) Floor[(Arg[I x + Sqrt[1 - x^2]] + Arg[Sqrt[y^2 + 1] - y])/(2 Pi)] + (-1)^Floor[1/2 - Arg[Sqrt[1 - x^2] Sqrt[y^2 + 1] - I x y]/Pi] + 2 (1 + (-1)^Floor[1/2 - Arg[Sqrt[1 - x^2] Sqrt[y^2 + 1] - I x y]/Pi]) Floor[1/2 - (Arg[I x + Sqrt[1 - x^2]] + Arg[Sqrt[y^2 + 1] - y])/ (2 Pi)]) - (1/2) (1 + (-1)^(-Floor[-(Arg[1 - x]/(2 Pi))])) (2 (-1 + (-1)^Floor[1/2 - Arg[I x y + Sqrt[1 - x^2] Sqrt[y^2 + 1]]/Pi]) Floor[(Arg[I x + Sqrt[1 - x^2]] + Arg[y + Sqrt[y^2 + 1]])/(2 Pi)] + (-1)^Floor[1/2 - Arg[I x y + Sqrt[1 - x^2] Sqrt[y^2 + 1]]/Pi] + 2 (1 + (-1)^Floor[1/2 - Arg[I x y + Sqrt[1 - x^2] Sqrt[y^2 + 1]]/Pi]) Floor[1/2 - (Arg[I x + Sqrt[1 - x^2]] + Arg[y + Sqrt[y^2 + 1]])/ (2 Pi)])) - (I Pi)/2

 Standard Form

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

 MathML Form

 cosh - 1 ( x ) - sinh - 1 ( y ) ( - 1 ) 1 2 - arg ( x - 1 x + 1 y 2 + 1 - x y ) π ( x y 2 + 1 - x - 1 x + 1 y ) + 1 - ( - 1 ) 1 2 - arg ( x - 1 x + 1 y 2 + 1 - x y ) π ( x y 2 + 1 - x - 1 x + 1 y ) - 1 cosh - 1 ( ( - 1 ) 1 2 - arg ( x - 1 x + 1 y 2 + 1 - x y ) π ( x - 1 x + 1 y - x y 2 + 1 ) ) - 1 2 π ( 1 2 ( 1 - ( - 1 ) - - arg ( 1 - x ) 2 π ) ( 2 ( - 1 + ( - 1 ) 1 2 - arg ( 1 - x 2 y 2 + 1 - x y ) π ) arg ( x + 1 - x 2 ) + arg ( y 2 + 1 - y ) 2 π + ( - 1 ) 1 2 - arg ( 1 - x 2 y 2 + 1 - x y ) π + 2 ( 1 + ( - 1 ) 1 2 - arg ( 1 - x 2 y 2 + 1 - x y ) π ) 1 2 - arg ( x + 1 - x 2 ) + arg ( y 2 + 1 - y ) 2 π ) - 1 2 ( 1 + ( - 1 ) - - arg ( 1 - x ) 2 π ) ( 2 ( - 1 + ( - 1 ) 1 2 - arg ( x y + y 2 + 1 1 - x 2 ) π ) arg ( y + y 2 + 1 ) + arg ( x + 1 - x 2 ) 2 π + ( - 1 ) 1 2 - arg ( x y + y 2 + 1 1 - x 2 ) π + 2 ( 1 + ( - 1 ) 1 2 - arg ( x y + y 2 + 1 1 - x 2 ) π ) 1 2 - arg ( y + y 2 + 1 ) + arg ( x + 1 - x 2 ) 2 π ) ) - π 2 x -1 y -1 1 2 -1 x -1 1 2 x 1 1 2 y 2 1 1 2 -1 x y -1 x y 2 1 1 2 -1 x -1 1 2 x 1 1 2 y 1 1 2 -1 -1 1 2 -1 x -1 1 2 x 1 1 2 y 2 1 1 2 -1 x y -1 x y 2 1 1 2 -1 x -1 1 2 x 1 1 2 y -1 1 2 -1 -1 1 2 -1 x -1 1 2 x 1 1 2 y 2 1 1 2 -1 x y -1 x -1 1 2 x 1 1 2 y -1 x y 2 1 1 2 -1 1 2 1 2 1 -1 -1 -1 -1 1 -1 x 2 -1 2 -1 -1 1 2 -1 1 -1 x 2 1 2 y 2 1 1 2 -1 x y -1 x 1 -1 x 2 1 2 y 2 1 1 2 -1 y 2 -1 -1 1 2 -1 1 -1 x 2 1 2 y 2 1 1 2 -1 x y -1 2 1 -1 1 2 -1 1 -1 x 2 1 2 y 2 1 1 2 -1 x y -1 1 2 -1 x 1 -1 x 2 1 2 y 2 1 1 2 -1 y 2 -1 -1 1 2 1 -1 -1 -1 1 -1 x 2 -1 2 -1 -1 1 2 -1 x y y 2 1 1 2 1 -1 x 2 1 2 -1 y y 2 1 1 2 x 1 -1 x 2 1 2 2 -1 -1 1 2 -1 x y y 2 1 1 2 1 -1 x 2 1 2 -1 2 1 -1 1 2 -1 x y y 2 1 1 2 1 -1 x 2 1 2 -1 1 2 -1 y y 2 1 1 2 x 1 -1 x 2 1 2 2 -1 -1 2 -1 [/itex]

 Rule Form

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

 2007-05-02