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; }

 ArcSech

 http://functions.wolfram.com/01.30.16.0250.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2007-05-02