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/01.26.16.0166.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

 2007-05-02