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 ArcCsch

 http://functions.wolfram.com/01.29.16.0247.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2007-05-02