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/01.26.16.0217.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2007-05-02