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/01.26.16.0205.01

 Input Form

 ArcCosh[x] - ArcSec[y] == -2 I Pi (Floor[(-Arg[x + Sqrt[x - 1] Sqrt[x + 1]] - Arg[(Sqrt[1 - 1/y^2] + I/y)^(-I)] + Pi)/(2 Pi)] + Floor[(Pi - Im[Log[x + Sqrt[x - 1] Sqrt[x + 1]]])/(2 Pi)] + Floor[(Re[Log[Sqrt[1 - 1/y^2] + I/y]] + Pi)/(2 Pi)]) + I Pi (1 - (-1)^(Floor[-(Arg[(x + Sqrt[x - 1] Sqrt[x + 1])/(Sqrt[1 - 1/y^2] + I/y)^ I + 1]/(2 Pi))] - Floor[-(Arg[(x + Sqrt[x - 1] Sqrt[x + 1])/(Sqrt[1 - 1/y^2] + I/y)^I]/ (2 Pi))])) + (-1)^(-Floor[-(Arg[(x + Sqrt[x - 1] Sqrt[x + 1])/(Sqrt[1 - 1/y^2] + I/y)^ I - 1]/(2 Pi))] + Floor[-(Arg[(x + Sqrt[x - 1] Sqrt[x + 1])/(Sqrt[1 - 1/y^2] + I/y)^I + 1]/ (2 Pi))] + Floor[-(Arg[(x + Sqrt[x - 1] Sqrt[x + 1])/ (Sqrt[1 - 1/y^2] + I/y)^I]/Pi)] + Floor[Arg[(x + Sqrt[x - 1] Sqrt[x + 1])/(Sqrt[1 - 1/y^2] + I/y)^I]/Pi - (2 Arg[(x + Sqrt[x - 1] Sqrt[x + 1])/(Sqrt[1 - 1/y^2] + I/y)^I - 1])/ Pi]) ArcCosh[(((x + Sqrt[x - 1] Sqrt[x + 1])^2/ (Sqrt[1 - 1/y^2] + I/y)^(2 I) + 1) (Sqrt[1 - 1/y^2] + I/y)^I)/ (2 (x + Sqrt[x - 1] Sqrt[x + 1]))] - Pi/2

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcCosh", "[", "x", "]"]], "-", RowBox[List["ArcSec", "[", "y", "]"]]]], "\[Equal]", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List["Floor", "[", FractionBox[RowBox[List[RowBox[List["-", RowBox[List["Arg", "[", RowBox[List["x", "+", RowBox[List[SqrtBox[RowBox[List["x", "-", "1"]]], " ", SqrtBox[RowBox[List["x", "+", "1"]]]]]]], "]"]]]], "-", RowBox[List["Arg", "[", SuperscriptBox[RowBox[List["(", RowBox[List[SqrtBox[RowBox[List["1", "-", FractionBox["1", SuperscriptBox["y", "2"]]]]], "+", FractionBox["\[ImaginaryI]", "y"]]], ")"]], RowBox[List["-", "\[ImaginaryI]"]]], "]"]], "+", "\[Pi]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]], "+", RowBox[List["Floor", "[", FractionBox[RowBox[List["\[Pi]", "-", RowBox[List["Im", "[", RowBox[List["Log", "[", RowBox[List["x", "+", RowBox[List[SqrtBox[RowBox[List["x", "-", "1"]]], " ", SqrtBox[RowBox[List["x", "+", "1"]]]]]]], "]"]], "]"]]]], RowBox[List["2", " ", "\[Pi]"]]], "]"]], "+", RowBox[List["Floor", "[", FractionBox[RowBox[List[RowBox[List["Re", "[", RowBox[List["Log", "[", RowBox[List[SqrtBox[RowBox[List["1", "-", FractionBox["1", SuperscriptBox["y", "2"]]]]], "+", FractionBox["\[ImaginaryI]", "y"]]], "]"]], "]"]], "+", "\[Pi]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]], ")"]]]], "+", RowBox[List["\[ImaginaryI]", " ", "\[Pi]", " ", RowBox[List["(", RowBox[List["1", "-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List[RowBox[List["Floor", "[", RowBox[List["-", FractionBox[RowBox[List["Arg", "[", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[SqrtBox[RowBox[List["1", "-", FractionBox["1", SuperscriptBox["y", "2"]]]]], "+", FractionBox["\[ImaginaryI]", "y"]]], ")"]], RowBox[List["-", "\[ImaginaryI]"]]], " ", RowBox[List["(", RowBox[List["x", "+", RowBox[List[SqrtBox[RowBox[List["x", "-", "1"]]], " ", SqrtBox[RowBox[List["x", "+", 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RowBox[List[SqrtBox[RowBox[List["1", "-", FractionBox["1", SuperscriptBox["y", "2"]]]]], "+", FractionBox["\[ImaginaryI]", "y"]]], ")"]], RowBox[List["-", "\[ImaginaryI]"]]]]], "-", "1"]], "]"]]]], "\[Pi]"]]], "]"]]]]], " ", RowBox[List["ArcCosh", "[", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[SqrtBox[RowBox[List["1", "-", FractionBox["1", SuperscriptBox["y", "2"]]]]], "+", FractionBox["\[ImaginaryI]", "y"]]], ")"]], RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["x", "+", RowBox[List[SqrtBox[RowBox[List["x", "-", "1"]]], " ", SqrtBox[RowBox[List["x", "+", "1"]]]]]]], ")"]], "2"]]], "+", "1"]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[SqrtBox[RowBox[List["1", "-", FractionBox["1", SuperscriptBox["y", "2"]]]]], "+", FractionBox["\[ImaginaryI]", "y"]]], ")"]], "\[ImaginaryI]"]]], RowBox[List["2", " ", RowBox[List["(", RowBox[List["x", "+", RowBox[List[SqrtBox[RowBox[List["x", "-", "1"]]], " ", SqrtBox[RowBox[List["x", "+", "1"]]]]]]], ")"]]]]], "]"]]]], "-", FractionBox["\[Pi]", "2"]]]]]]]

 MathML Form

 cosh - 1 ( x ) - sec - 1 ( y ) - 2 π ( - arg ( x + x - 1 x + 1 ) - arg ( ( 1 - 1 y 2 + y ) - ) + π 2 π + Re ( log ( 1 - 1 y 2 + y ) ) + π 2 π + π - Im ( log ( x + x - 1 x + 1 ) ) 2 π ) + π ( 1 - ( - 1 ) - arg ( ( x + x - 1 x + 1 ) ( 1 - 1 y 2 + y ) - + 1 ) 2 π - - arg ( ( x + x - 1 x + 1 ) ( 1 - 1 y 2 + y ) - ) 2 π ) + ( - 1 ) arg ( ( x + x - 1 x + 1 ) ( 1 - 1 y 2 + y ) - ) π - 2 arg ( ( x + x - 1 x + 1 ) ( 1 - 1 y 2 + y ) - - 1 ) π + - arg ( ( x + x - 1 x + 1 ) ( 1 - 1 y 2 + y ) - ) π - - arg ( ( x + x - 1 x + 1 ) ( 1 - 1 y 2 + y ) - - 1 ) 2 π + - arg ( ( x + x - 1 x + 1 ) ( 1 - 1 y 2 + y ) - + 1 ) 2 π cosh - 1 ( ( ( x + x - 1 x + 1 ) 2 ( 1 - 1 y 2 + y ) - 2 + 1 ) ( 1 - 1 y 2 + y ) 2 ( x + x - 1 x + 1 ) ) - π 2 x -1 y -2 -1 x x -1 1 2 x 1 1 2 -1 1 -1 1 y 2 -1 1 2 y -1 -1 2 -1 1 -1 1 y 2 -1 1 2 y -1 2 -1 -1 x x -1 1 2 x 1 1 2 2 -1 1 -1 -1 -1 x x -1 1 2 x 1 1 2 1 -1 1 y 2 -1 1 2 y -1 -1 1 2 -1 -1 -1 x x -1 1 2 x 1 1 2 1 -1 1 y 2 -1 1 2 y -1 -1 2 -1 -1 x x -1 1 2 x 1 1 2 1 -1 1 y 2 -1 1 2 y -1 -1 -1 -1 2 x x -1 1 2 x 1 1 2 1 -1 1 y 2 -1 1 2 y -1 -1 -1 -1 -1 x x -1 1 2 x 1 1 2 1 -1 1 y 2 -1 1 2 y -1 -1 -1 -1 -1 x x -1 1 2 x 1 1 2 1 -1 1 y 2 -1 1 2 y -1 -1 -1 2 -1 -1 x x -1 1 2 x 1 1 2 1 -1 1 y 2 -1 1 2 y -1 -1 1 2 -1 x x -1 1 2 x 1 1 2 2 1 -1 1 y 2 -1 1 2 y -1 -2 1 1 -1 1 y 2 -1 1 2 y -1 2 x x -1 1 2 x 1 1 2 -1 -1 2 -1 [/itex]

 Rule Form

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

 2007-05-02