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\begin{document}
\noindent
The inverse function of the polynomial expansion ~~$y = f(x) = ax+bx^2+cx^3
+dx^4 + ex^5 + fx^6+\cdots$ $(a\ne0)$ begins with the elements
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\begin{eqnarray*}
x = \varphi(y) = \frac{1}{a}y &-& \frac{b}{a^3}y^2 + \frac{1}{a^5}(2b^2-ac)y^3\\
   &+&\frac{1}{a^7}(5abc - z^2d -fb^3)y^4\\ 
   &+&\frac{1}{a^9}(6a^2bd + 3a^2c^2+14b^4 - a^3e - 21ab^2c)y^5\\
   &+&\frac{1}{a^{11}}(7a^3be + 7a^3cd + 84ab^3c - a^4f -\\
   &&28a^2b^2d -28 a^2bc^2 - 43b^5)y^6 + \cdots
\end{eqnarray*}
\end{document}
