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/01.26.16.0172.01

 Input Form

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

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcCosh", "[", "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["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[RowBox[List["Arg", "[", FractionBox[RowBox[List["x", "+", RowBox[List["\[ImaginaryI]", " ", SqrtBox[RowBox[List["x", "-", "1"]]], " ", SqrtBox[RowBox[List["x", "+", "1"]]], " ", "y"]]]], SqrtBox[RowBox[List[SuperscriptBox["y", "2"], "+", "1"]]]], "]"]], "\[Pi]"]]], "]"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "x", " ", "y"]], "+", RowBox[List[SqrtBox[RowBox[List["x", "-", "1"]]], " ", SqrtBox[RowBox[List["x", "+", "1"]]]]]]], ")"]]]], SqrtBox[RowBox[List[SuperscriptBox["y", "2"], "+", 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FractionBox[RowBox[List["\[ImaginaryI]", "-", "y"]], SqrtBox[RowBox[List[SuperscriptBox["y", "2"], "+", "1"]]]], "]"]]]], RowBox[List["2", " ", "\[Pi]"]]]]], "]"]]]], "-", "1"]], ")"]]]], "-", RowBox[List[FractionBox["1", "4"], " ", 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]"]]]]], "]"]]]]]]], ")"]], " ", "\[Pi]", " ", "\[ImaginaryI]", RowBox[List["(", RowBox[List[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", "[", FractionBox[RowBox[List["x", "-", RowBox[List[SqrtBox[RowBox[List["1", "-", SuperscriptBox["x", "2"]]]], " ", "y"]]]], SqrtBox[RowBox[List[SuperscriptBox["y", "2"], "+", "1"]]]], "]"]], 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RowBox[List[FractionBox["1", "2"], "-", FractionBox[RowBox[List["Arg", "[", FractionBox[RowBox[List["x", "-", RowBox[List[SqrtBox[RowBox[List["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[RowBox[List["\[ImaginaryI]", " ", "x"]], "+", SqrtBox[RowBox[List["1", "-", SuperscriptBox["x", "2"]]]]]], "]"]], "+", RowBox[List["Arg", "[", FractionBox[RowBox[List["y", "+", "\[ImaginaryI]"]], SqrtBox[RowBox[List[SuperscriptBox["y", "2"], "+", "1"]]]], "]"]]]], RowBox[List["2", " ", "\[Pi]"]]]]], "]"]]]], "-", "1"]], ")"]]]]]]]]]]

 MathML Form

 cosh - 1 ( x ) + tan - 1 ( y ) 1 - ( - 1 ) 1 2 - arg ( x + x - 1 x + 1 y y 2 + 1 ) π ( x y + x - 1 x + 1 ) y 2 + 1 ( - 1 ) 1 2 - arg ( x + x - 1 x + 1 y y 2 + 1 ) π ( x y + x - 1 x + 1 ) y 2 + 1 - 1 cosh - 1 ( ( - 1 ) 1 2 - arg ( x + x - 1 x + 1 y y 2 + 1 ) π ( x y + x - 1 x + 1 ) y 2 + 1 ) - π 2 + 1 4 ( 1 - ( - 1 ) - - arg ( 1 - x ) 2 π ) π ( 2 ( 1 + ( - 1 ) 1 2 - arg ( x + 1 - x 2 y y 2 + 1 ) π ) arg ( - y y 2 + 1 ) + arg ( x + 1 - x 2 ) 2 π + ( - 1 ) 1 2 - arg ( x + 1 - x 2 y y 2 + 1 ) π - 2 ( - 1 + ( - 1 ) 1 2 - arg ( x + 1 - x 2 y y 2 + 1 ) π ) 1 2 - arg ( - y y 2 + 1 ) + arg ( x + 1 - x 2 ) 2 π - 1 ) - 1 4 ( 1 + ( - 1 ) - - arg ( 1 - x ) 2 π ) π ( 2 ( 1 + ( - 1 ) 1 2 - arg ( x - 1 - x 2 y y 2 + 1 ) π ) arg ( y + y 2 + 1 ) + arg ( x + 1 - x 2 ) 2 π + ( - 1 ) 1 2 - arg ( x - 1 - x 2 y y 2 + 1 ) π - 2 ( - 1 + ( - 1 ) 1 2 - arg ( x - 1 - x 2 y y 2 + 1 ) π ) 1 2 - arg ( y + y 2 + 1 ) + arg ( x + 1 - x 2 ) 2 π - 1 ) x y 1 -1 -1 1 2 -1 x x -1 1 2 x 1 1 2 y y 2 1 1 2 -1 -1 x y x -1 1 2 x 1 1 2 y 2 1 1 2 -1 1 2 -1 1 2 -1 x x -1 1 2 x 1 1 2 y y 2 1 1 2 -1 -1 x y x -1 1 2 x 1 1 2 y 2 1 1 2 -1 -1 1 2 -1 -1 1 2 -1 x x -1 1 2 x 1 1 2 y y 2 1 1 2 -1 -1 x y x -1 1 2 x 1 1 2 y 2 1 1 2 -1 -1 2 -1 1 4 1 -1 -1 -1 -1 1 -1 x 2 -1 2 1 -1 1 2 -1 x 1 -1 x 2 1 2 y y 2 1 1 2 -1 -1 -1 y y 2 1 1 2 -1 x 1 -1 x 2 1 2 2 -1 -1 1 2 -1 x 1 -1 x 2 1 2 y y 2 1 1 2 -1 -1 -1 2 -1 -1 1 2 -1 x 1 -1 x 2 1 2 y y 2 1 1 2 -1 -1 1 2 -1 -1 y y 2 1 1 2 -1 x 1 -1 x 2 1 2 2 -1 -1 -1 1 4 1 -1 -1 -1 1 -1 x 2 -1 2 1 -1 1 2 -1 x -1 1 -1 x 2 1 2 y y 2 1 1 2 -1 -1 y y 2 1 1 2 -1 x 1 -1 x 2 1 2 2 -1 -1 1 2 -1 x -1 1 -1 x 2 1 2 y y 2 1 1 2 -1 -1 -1 2 -1 -1 1 2 -1 x -1 1 -1 x 2 1 2 y y 2 1 1 2 -1 -1 1 2 -1 y y 2 1 1 2 -1 x 1 -1 x 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["ArcTan", "[", "y_", "]"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", SqrtBox[RowBox[List["1", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[RowBox[List["Arg", "[", FractionBox[RowBox[List["x", "+", RowBox[List["\[ImaginaryI]", " ", SqrtBox[RowBox[List["x", "-", "1"]]], " ", SqrtBox[RowBox[List["x", "+", "1"]]], " ", "y"]]]], SqrtBox[RowBox[List[SuperscriptBox["y", "2"], "+", "1"]]]], "]"]], "\[Pi]"]]], "]"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "x", " ", "y"]], "+", RowBox[List[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