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: 10px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 ArcCosh

 http://functions.wolfram.com/01.26.16.0171.01

 Input Form

 ArcCosh[x] + ArcTan[y] == -2 I Pi (Floor[(-Arg[x + Sqrt[x - 1] Sqrt[x + 1]] - Arg[(1 - I y)^(I/2)] + Pi)/(2 Pi)] + Floor[(Pi - Im[Log[x + Sqrt[x - 1] Sqrt[x + 1]]])/ (2 Pi)] + Floor[(Pi - (1/2) Re[Log[1 - I y]])/(2 Pi)]) - 2 I Pi (Floor[(-Arg[(x + Sqrt[x - 1] Sqrt[x + 1]) (1 - I y)^(I/2)] - Arg[(I y + 1)^(-(I/2))] + Pi)/(2 Pi)] + Floor[(Pi - Im[Log[(x + Sqrt[x - 1] Sqrt[x + 1]) (1 - I y)^(I/2)]])/ (2 Pi)] + Floor[((1/2) Re[Log[I y + 1]] + Pi)/(2 Pi)]) + I Pi (1 - (-1)^(Floor[-(Arg[((1 - I y)^(I/2) (x + Sqrt[x - 1] Sqrt[x + 1]))/ (I y + 1)^(I/2) + 1]/(2 Pi))] - Floor[-(Arg[((x + Sqrt[x - 1] Sqrt[x + 1]) (1 - I y)^(I/2))/ (I y + 1)^(I/2)]/(2 Pi))])) + (-1)^(-Floor[-(Arg[((x + Sqrt[x - 1] Sqrt[x + 1]) (1 - I y)^(I/2))/ (I y + 1)^(I/2) - 1]/(2 Pi))] + Floor[-(Arg[((1 - I y)^(I/2) (x + Sqrt[x - 1] Sqrt[x + 1]))/ (I y + 1)^(I/2) + 1]/(2 Pi))] + Floor[-(Arg[((x + Sqrt[x - 1] Sqrt[x + 1]) (1 - I y)^(I/2))/ (I y + 1)^(I/2)]/Pi)] + Floor[Arg[((x + Sqrt[x - 1] Sqrt[x + 1]) (1 - I y)^(I/2))/ (I y + 1)^(I/2)]/Pi - (2 Arg[((x + Sqrt[x - 1] Sqrt[x + 1]) (1 - I y)^(I/2))/ (I y + 1)^(I/2) - 1])/Pi]) ArcCosh[((((1 - I y)^I (x + Sqrt[x - 1] Sqrt[x + 1])^2)/(I y + 1)^I + 1) (I y + 1)^(I/2))/((1 - I y)^(I/2) (2 (x + Sqrt[x - 1] Sqrt[x + 1])))]

 Standard Form

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 MathML Form

 cosh - 1 ( x ) + tan - 1 ( y ) - 2 π ( - arg ( ( y + 1 ) - 2 ) - arg ( ( x + x - 1 x + 1 ) ( 1 - y ) / 2 ) + π 2 π + 1 2 Re ( log ( y + 1 ) ) + π 2 π + π - Im ( log ( ( x + x - 1 x + 1 ) ( 1 - y ) / 2 ) ) 2 π ) - 2 π ( - arg ( x + x - 1 x + 1 ) - arg ( ( 1 - y ) / 2 ) + π 2 π + π - Im ( log ( x + x - 1 x + 1 ) ) 2 π + π - 1 2 Re ( log ( 1 - y ) ) 2 π ) + π ( 1 - ( - 1 ) - arg ( ( y + 1 ) - 2 ( x + x - 1 x + 1 ) ( 1 - y ) / 2 + 1 ) 2 π - - arg ( ( x + x - 1 x + 1 ) ( 1 - y ) / 2 ( y + 1 ) - 2 ) 2 π ) + ( - 1 ) arg ( ( x + x - 1 x + 1 ) ( 1 - y ) / 2 ( y + 1 ) - 2 ) π - 2 arg ( ( x + x - 1 x + 1 ) ( 1 - y ) / 2 ( y + 1 ) - 2 - 1 ) π + - arg ( ( x + x - 1 x + 1 ) ( 1 - y ) / 2 ( y + 1 ) - 2 ) π - - arg ( ( x + x - 1 x + 1 ) ( 1 - y ) / 2 ( y + 1 ) - 2 - 1 ) 2 π + - arg ( ( y + 1 ) - 2 ( x + x - 1 x + 1 ) ( 1 - y ) / 2 + 1 ) 2 π cosh - 1 ( ( ( x + x - 1 x + 1 ) 2 ( 1 - y ) ( y + 1 ) - + 1 ) ( 1 - y ) - 2 ( y + 1 ) / 2 2 ( x + x - 1 x + 1 ) ) x y -2 -1 y 1 -1 2 -1 -1 x x -1 1 2 x 1 1 2 1 -1 y 2 -1 2 -1 1 2 y 1 2 -1 -1 x x -1 1 2 x 1 1 2 1 -1 y 2 -1 2 -1 -1 2 -1 x x -1 1 2 x 1 1 2 -1 1 -1 y 2 -1 2 -1 -1 x x -1 1 2 x 1 1 2 2 -1 -1 1 2 1 -1 y 2 -1 1 -1 -1 -1 y 1 -1 2 -1 x x -1 1 2 x 1 1 2 1 -1 y 2 -1 1 2 -1 -1 -1 x x -1 1 2 x 1 1 2 1 -1 y 2 -1 y 1 -1 2 -1 2 -1 -1 x x -1 1 2 x 1 1 2 1 -1 y 2 -1 y 1 -1 2 -1 -1 -1 2 x x -1 1 2 x 1 1 2 1 -1 y 2 -1 y 1 -1 2 -1 -1 -1 -1 x x -1 1 2 x 1 1 2 1 -1 y 2 -1 y 1 -1 2 -1 -1 -1 -1 x x -1 1 2 x 1 1 2 1 -1 y 2 -1 y 1 -1 2 -1 -1 2 -1 -1 y 1 -1 2 -1 x x -1 1 2 x 1 1 2 1 -1 y 2 -1 1 2 -1 x x -1 1 2 x 1 1 2 2 1 -1 y y 1 -1 1 1 -1 y -1 2 -1 y 1 2 -1 2 x x -1 1 2 x 1 1 2 -1 [/itex]

 Rule Form

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

 2007-05-02