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/01.30.16.0218.01

 Input Form

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

 Standard Form

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

 MathML Form

 sech - 1 ( x ) - tan - 1 ( y ) 1 - ( - 1 ) 1 2 - arg ( 1 x - 1 x - 1 1 + 1 x y y 2 + 1 ) π ( y x + 1 x - 1 1 + 1 x ) y 2 + 1 ( - 1 ) 1 2 - arg ( 1 x - 1 x - 1 1 + 1 x y y 2 + 1 ) π ( y x + 1 x - 1 1 + 1 x ) y 2 + 1 - 1 sech - 1 ( ( - 1 ) - 1 2 - arg ( 1 x - 1 x - 1 1 + 1 x y y 2 + 1 ) π y 2 + 1 y x + 1 x - 1 1 + 1 x ) - 1 4 ( 1 + ( - 1 ) - - arg ( 1 - 1 x ) 2 π ) π ( 2 ( 1 + ( - 1 ) 1 2 - arg ( 1 - 1 x 2 y + 1 x y 2 + 1 ) π ) arg ( - y y 2 + 1 ) + arg ( 1 - 1 x 2 + x ) 2 π + ( - 1 ) 1 2 - arg ( 1 - 1 x 2 y + 1 x y 2 + 1 ) π - 2 ( - 1 + ( - 1 ) 1 2 - arg ( 1 - 1 x 2 y + 1 x y 2 + 1 ) π ) 1 2 - arg ( - y y 2 + 1 ) + arg ( 1 - 1 x 2 + x ) 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 y 2 + 1 ) π ) arg ( y + y 2 + 1 ) + arg ( 1 - 1 x 2 + x ) 2 π + ( - 1 ) 1 2 - arg ( 1 x - 1 - 1 x 2 y y 2 + 1 ) π - 2 ( - 1 + ( - 1 ) 1 2 - arg ( 1 x - 1 - 1 x 2 y y 2 + 1 ) π ) 1 2 - arg ( y + y 2 + 1 ) + arg ( 1 - 1 x 2 + x ) 2 π - 1 ) - π 2 x -1 y 1 -1 -1 1 2 -1 1 x -1 -1 1 x -1 -1 1 2 1 1 x -1 1 2 y y 2 1 1 2 -1 -1 y x -1 1 x -1 -1 1 2 1 1 x -1 1 2 y 2 1 1 2 -1 1 2 -1 1 2 -1 1 x -1 -1 1 x -1 -1 1 2 1 1 x -1 1 2 y y 2 1 1 2 -1 -1 y x -1 1 x -1 -1 1 2 1 1 x -1 1 2 y 2 1 1 2 -1 -1 1 2 -1 -1 -1 1 2 -1 1 x -1 -1 1 x -1 -1 1 2 1 1 x -1 1 2 y y 2 1 1 2 -1 -1 y 2 1 1 2 y x -1 1 x -1 -1 1 2 1 1 x -1 1 2 -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 x -1 y 2 1 1 2 -1 -1 -1 y y 2 1 1 2 -1 1 -1 1 x 2 -1 1 2 x -1 2 -1 -1 1 2 -1 1 -1 1 x 2 -1 1 2 y 1 x -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 x -1 y 2 1 1 2 -1 -1 1 2 -1 -1 y y 2 1 1 2 -1 1 -1 1 x 2 -1 1 2 x -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 y 2 1 1 2 -1 -1 y y 2 1 1 2 -1 1 -1 1 x 2 -1 1 2 x -1 2 -1 -1 1 2 -1 1 x -1 -1 1 -1 1 x 2 -1 1 2 y 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 y 2 1 1 2 -1 -1 1 2 -1 y y 2 1 1 2 -1 1 -1 1 x 2 -1 1 2 x -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["\[ImaginaryI]", " ", RowBox[List["ArcTan", "[", "y_", "]"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["(", 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["1", "x"], "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox[RowBox[List[FractionBox["1", "x"], "-", "1"]]], " ", SqrtBox[RowBox[List["1", "+", FractionBox["1", "x"]]]], " ", "y"]]]], SqrtBox[RowBox[List[SuperscriptBox["y", "2"], "+", "1"]]]], "]"]], "\[Pi]"]]], "]"]]], " ", RowBox[List["(", RowBox[List[FractionBox["y", "x"], "+", RowBox[List["\[ImaginaryI]", " ", SqrtBox[RowBox[List[FractionBox["1", "x"], "-", "1"]]], " ", 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 Date Added to functions.wolfram.com (modification date)

 2007-05-02