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 ArcCsch

 http://functions.wolfram.com/01.29.16.0233.01

 Input Form

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

 Standard Form

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 MathML Form

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 Rule Form

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

 2007-05-02