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

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