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/01.12.16.0214.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

 2007-05-02