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/01.30.16.0206.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

 2007-05-02