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gfun

 ratpolytocoeff
 compute the nth coefficient of a rational function

 Calling Sequence ratpolytocoeff(f, x, n)

Parameters

 f - rational function in x x - name; indeterminate in f n - name; index of the Taylor coefficients

Description

 • The ratpolytocoeff(f, x, n) command computes the expression for the nth coefficient of the Taylor expansion about the origin of f as a function of x.

Examples

 > $\mathrm{with}\left(\mathrm{gfun}\right):$
 > $\mathrm{ratpolytocoeff}\left(\frac{1}{1-x-{x}^{2}},x,n\right)$
 ${\sum }_{{\mathrm{_α}}{=}{\mathrm{RootOf}}{}\left({{\mathrm{_Z}}}^{{2}}{+}{\mathrm{_Z}}{-}{1}\right)}\phantom{\rule[-0.0ex]{5.0px}{0.0ex}}\left({-}\frac{\left({-}\frac{{2}}{{5}}{}{\mathrm{_α}}{-}\frac{{1}}{{5}}\right){}{{\mathrm{_α}}}^{{-}{n}}}{{\mathrm{_α}}}\right)$ (1)

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