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; }

 ArcSech

 http://functions.wolfram.com/01.30.16.0232.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

 2007-05-02