The compositional inverse (with respect to x) of
y(t, x) = x - t*(exp(x) - 1)
is
1/(1-t)*y + t/(1-t)^3*y^2/2! + (t+2*t^2)/(1-t)^5*y^3/3! +
(t+8*t^2+6*t^3)/(1-t)^7*y^4/4! + ...
Apparently multivariate power series rings do not know how
to reverse a series.
Perhaps there is a workaround?
Thanks!
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