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http://functions.wolfram.com/01.18.16.0209.01
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a ArcSec[x] + b ArcCsch[y] ==
(Pi a)/2 - 2 I Pi (Floor[(-Arg[(Sqrt[1 - 1/x^2] + I/x)^(I a)] -
Arg[(Sqrt[1 + 1/y^2] + 1/y)^b] + Pi)/(2 Pi)] +
Floor[(Pi - Im[b Log[Sqrt[1 + 1/y^2] + 1/y]])/(2 Pi)] +
Floor[(Pi - Re[a Log[Sqrt[1 - 1/x^2] + I/x]])/(2 Pi)]) +
I
(1 - (-1)^(Floor[-(Arg[(Sqrt[1 + 1/y^2] + 1/y)^b (Sqrt[1 - 1/x^2] + I/x)^
(I a) + 1]/(2 Pi))] -
Floor[-(Arg[(Sqrt[1 - 1/x^2] + I/x)^(I a) (Sqrt[1 + 1/y^2] + 1/y)^b]/
(2 Pi))])) Pi -
I (-1)^(Floor[Arg[(Sqrt[1 - 1/x^2] + I/x)^(I a) (Sqrt[1 + 1/y^2] + 1/y)^b -
1]/(2 Pi) - Arg[(Sqrt[1 + 1/y^2] + 1/y)^b (Sqrt[1 - 1/x^2] + I/x)^
(I a) + 1]/(2 Pi) + 1/2] +
Floor[-(Arg[(Sqrt[1 - 1/x^2] + I/x)^(I a) (Sqrt[1 + 1/y^2] + 1/y)^b]/
Pi)]) ArcSec[(2 (Sqrt[1 - 1/x^2] + I/x)^(I a)
(Sqrt[1 + 1/y^2] + 1/y)^b)/((Sqrt[1 + 1/y^2] + 1/y)^(2 b)
(Sqrt[1 - 1/x^2] + I/x)^(2 I a) + 1)]
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