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; }

 ArcCsc

 http://functions.wolfram.com/01.17.16.0208.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

 2007-05-02