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

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2007-05-02