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; }

 ArcSin

 http://functions.wolfram.com/01.12.16.0114.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

 2007-05-02