E.g.f. C(x) and related series S(x) satisfy the following relations.
(1a) S(x) = Integral C(x) * C(S(x)) dx.
(1b) C(x) = 1 + Integral S(x) * C(S(x)) dx.
(2) C(x)^2 - S(x)^2 = 1.
(3a) d/dx S(x) = C(x) * C(S(x)).
(3b) d/dx C(x) = S(x) * C(S(x)).
(4a) C(x) + S(x) = exp( Integral C(S(x)) dx ).
(4b) C(x) = cosh( Integral C(S(x)) dx ).
(4c) S(x) = sinh( Integral C(S(x)) dx ).
(5) C(S(x))^2 - S(S(x))^2 = 1.
(5a) S(S(x)) = Integral C(x) * C(S(x))^2 * C(S(S(x))) dx.
(5b) C(S(x)) = 1 + Integral C(x) * S(S(x)) * C(S(x)) * C(S(S(x))) dx.
(6a) C(S(x)) + S(S(x)) = exp( Integral C(x) * C(S(x)) * C(S(S(x))) dx ).
(6b) C(S(x)) = cosh( Integral C(x) * C(S(x)) * C(S(S(x))) dx ).
(6c) S(S(x)) = sinh( Integral C(x) * C(S(x)) * C(S(S(x))) dx ).
(7) C(S(S(x))) + S(S(S(x))) = exp( Integral C(x) * C(S(x))^2 * C(S(S(x))) * C(S(S(S(x)))) dx ).
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