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diff --git a/Master/texmf-dist/doc/latex/guide-to-latex/exercises/chap7/exer7-18.tex b/Master/texmf-dist/doc/latex/guide-to-latex/exercises/chap7/exer7-18.tex new file mode 100644 index 00000000000..7abf3d9221d --- /dev/null +++ b/Master/texmf-dist/doc/latex/guide-to-latex/exercises/chap7/exer7-18.tex @@ -0,0 +1,14 @@ +\documentclass{article} +\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 +\setlength{\arraycolsep}{2pt} +\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} |