Theta-curve polynomials and finite-type invariants

The normalized Yamada polynomial is a polynomial invariant in variable A for theta-curves. In this work, we show that the coefficients of the power series obtained from this polynomial by the substitution A=e^x=1+x+x^2/2+x^3/6+... are finite-type invariants for theta-curves although the coefficients of original polynomial are not. A similar result can be obtained in the case of Yokota polynomial for theta-curves.