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

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2007-05-02