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/01.26.16.0186.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

 2007-05-02