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; }

 ArcCos

 http://functions.wolfram.com/01.13.16.0208.01

 Input Form

 a ArcCos[x] + b ArcCot[y] == (Pi a)/2 - 2 I Pi (Floor[(-Arg[(I x + Sqrt[1 - x^2])^(I a)] - Arg[(1 - I/y)^((I b)/2)] + Pi)/(2 Pi)] + Floor[(Pi - Re[a Log[I x + Sqrt[1 - x^2]]])/(2 Pi)] + Floor[(Pi - (1/2) Re[b Log[1 - I/y]])/(2 Pi)]) - 2 I Pi (Floor[(-Arg[(I x + Sqrt[1 - x^2])^(I a) (1 - I/y)^((I b)/2)] - Arg[(1 + I/y)^((-(1/2)) (I b))] + Pi)/(2 Pi)] + Floor[(Pi - Im[Log[(I x + Sqrt[1 - x^2])^(I a) (1 - I/y)^((I b)/2)]])/ (2 Pi)] + Floor[((1/2) Re[b Log[1 + I/y]] + Pi)/(2 Pi)]) + I (1 - (-1)^(Floor[-(Arg[((1 - I/y)^((I b)/2) (I x + Sqrt[1 - x^2])^(I a))/ (1 + I/y)^((1/2) (I b)) + 1]/(2 Pi))] - Floor[-(Arg[((I x + Sqrt[1 - x^2])^(I a) (1 - I/y)^((I b)/2))/ (1 + I/y)^((1/2) (I b))]/(2 Pi))])) Pi - I (-1)^(Floor[Arg[((I x + Sqrt[1 - x^2])^(I a) (1 - I/y)^((I b)/2))/ (1 + I/y)^((1/2) (I b)) - 1]/(2 Pi) - Arg[((1 - I/y)^((I b)/2) (I x + Sqrt[1 - x^2])^(I a))/ (1 + I/y)^((1/2) (I b)) + 1]/(2 Pi) + 1/2] + Floor[-(Arg[((I x + Sqrt[1 - x^2])^(I a) (1 - I/y)^((I b)/2))/ (1 + I/y)^((1/2) (I b))]/Pi)]) ArcCos[((1/2) (((1 - I/y)^(I b) (I x + Sqrt[1 - x^2])^(2 I a))/ (1 + I/y)^(I b) + 1) (1 + I/y)^((I b)/2))/ ((I x + Sqrt[1 - x^2])^(I a) (1 - I/y)^((1/2) (I b)))]

 Standard Form

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

 MathML Form

 a cos - 1 ( x ) + b cot - 1 ( y ) π a 2 - ( - 1 ) arg ( ( x + 1 - x 2 ) a ( 1 - y ) b 2 ( 1 + y ) - 1 2 ( b ) - 1 ) 2 π + 1 2 - arg ( ( x + 1 - x 2 ) a ( 1 + y ) - 1 2 ( b ) ( 1 - y ) b 2 + 1 ) 2 π + - arg ( ( x + 1 - x 2 ) a ( 1 - y ) b 2 ( 1 + y ) - 1 2 ( b ) ) π cos - 1 ( 1 2 ( x + 1 - x 2 ) - a ( ( 1 + y ) - b ( 1 - y ) b ( x + 1 - x 2 ) 2 a + 1 ) ( 1 - y ) - 1 2 ( b ) ( 1 + y ) b 2 ) - 2 π ( - arg ( ( 1 + y ) - 1 2 ( b ) ) - arg ( ( x + 1 - x 2 ) a ( 1 - y ) b 2 ) + π 2 π + 1 2 Re ( b log ( 1 + y ) ) + π 2 π + π - Im ( log ( ( x + 1 - x 2 ) a ( 1 - y ) b 2 ) ) 2 π ) - 2 π ( - arg ( ( x + 1 - x 2 ) a ) - arg ( ( 1 - y ) b 2 ) + π 2 π + π - Re ( a log ( x + 1 - x 2 ) ) 2 π + π - 1 2 Re ( b log ( 1 - y ) ) 2 π ) + ( 1 - ( - 1 ) - arg ( ( x + 1 - x 2 ) a ( 1 + y ) - 1 2 ( b ) ( 1 - y ) b 2 + 1 ) 2 π - - arg ( ( x + 1 - x 2 ) a ( 1 - y ) b 2 ( 1 + y ) - 1 2 ( b ) ) 2 π ) π a x b y a 2 -1 -1 -1 x 1 -1 x 2 1 2 a 1 -1 y -1 b 2 -1 1 y -1 -1 1 2 b -1 2 -1 1 2 -1 x 1 -1 x 2 1 2 a 1 y -1 -1 1 2 b 1 -1 y -1 b 2 -1 1 2 -1 -1 x 1 -1 x 2 1 2 a 1 -1 y -1 b 2 -1 1 y -1 -1 1 2 b -1 1 2 x 1 -1 x 2 1 2 -1 a 1 y -1 -1 b 1 -1 y -1 b x 1 -1 x 2 1 2 2 a 1 1 -1 y -1 -1 1 2 b 1 y -1 b 2 -1 -1 2 -1 1 y -1 -1 1 2 b -1 x 1 -1 x 2 1 2 a 1 -1 y -1 b 2 -1 2 -1 1 2 b 1 y -1 2 -1 -1 x 1 -1 x 2 1 2 a 1 -1 y -1 b 2 -1 2 -1 -1 2 -1 x 1 -1 x 2 1 2 a -1 1 -1 y -1 b 2 -1 2 -1 -1 a x 1 -1 x 2 1 2 2 -1 -1 1 2 b 1 -1 y -1 2 -1 1 -1 -1 -1 x 1 -1 x 2 1 2 a 1 y -1 -1 1 2 b 1 -1 y -1 b 2 -1 1 2 -1 -1 -1 x 1 -1 x 2 1 2 a 1 -1 y -1 b 2 -1 1 y -1 -1 1 2 b 2 -1 [/itex]

 Rule Form

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 Date Added to functions.wolfram.com (modification date)

 2007-05-02