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 ArcCsch

 http://functions.wolfram.com/01.29.16.0243.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2007-05-02