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/01.13.16.0217.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["a_", " ", RowBox[List["ArcCos", "[", "x_", "]"]]]], "+", RowBox[List["b_", " ", RowBox[List["ArcTanh", "[", "y_", "]"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["\[Pi]", " ", "a"]], "2"], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List["Floor", "[", FractionBox[RowBox[List[RowBox[List["-", RowBox[List["Arg", "[", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "x"]], "+", SqrtBox[RowBox[List["1", "-", SuperscriptBox["x", "2"]]]]]], ")"]], RowBox[List["\[ImaginaryI]", " ", "a"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "y"]], ")"]], RowBox[List["-", FractionBox["b", "2"]]]]]], "]"]]]], "-", RowBox[List["Arg", "[", SuperscriptBox[RowBox[List["(", RowBox[List["y", "+", "1"]], ")"]], RowBox[List["b", "/", "2"]]], "]"]], "+", "\[Pi]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]], "+", RowBox[List["Floor", "[", FractionBox[RowBox[List["\[Pi]", "-", RowBox[List["Im", "[", RowBox[List["Log", "[", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "x"]], "+", SqrtBox[RowBox[List["1", "-", SuperscriptBox["x", "2"]]]]]], ")"]], RowBox[List["\[ImaginaryI]", " ", "a"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "y"]], ")"]], RowBox[List["-", FractionBox["b", "2"]]]]]], "]"]], "]"]]]], RowBox[List["2", " ", "\[Pi]"]]], "]"]], "+", RowBox[List["Floor", "[", FractionBox[RowBox[List["\[Pi]", "-", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["Im", "[", RowBox[List["b", " ", RowBox[List["Log", "[", RowBox[List["y", "+", "1"]], "]"]]]], "]"]]]]]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]], ")"]]]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List["Floor", "[", FractionBox[RowBox[List[RowBox[List["-", RowBox[List["Arg", "[", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "x"]], "+", SqrtBox[RowBox[List["1", "-", SuperscriptBox["x", "2"]]]]]], ")"]], RowBox[List["\[ImaginaryI]", " ", "a"]]], "]"]]]], "-", RowBox[List["Arg", "[", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "y"]], ")"]], RowBox[List["-", FractionBox["b", "2"]]]], "]"]], "+", "\[Pi]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]], "+", RowBox[List["Floor", "[", FractionBox[RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["Im", "[", RowBox[List["b", " ", RowBox[List["Log", "[", RowBox[List["1", "-", "y"]], "]"]]]], "]"]]]], "+", "\[Pi]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]], "+", RowBox[List["Floor", "[", FractionBox[RowBox[List["\[Pi]", "-", RowBox[List["Re", "[", RowBox[List["a", " ", RowBox[List["Log", "[", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "x"]], "+", SqrtBox[RowBox[List["1", "-", SuperscriptBox["x", "2"]]]]]], "]"]]]], "]"]]]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]], ")"]]]], "+", RowBox[List["Log", "[", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "x"]], "+", SqrtBox[RowBox[List["1", "-", SuperscriptBox["x", "2"]]]]]], ")"]], RowBox[List["\[ImaginaryI]", " ", "a"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "y"]], ")"]], RowBox[List["-", FractionBox["b", "2"]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["y", "+", "1"]], ")"]], RowBox[List["b", "/", "2"]]]]], "]"]]]]]]]]

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

 2007-05-02