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/01.26.16.0219.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2007-05-02