Binomial Coefficients and Generating Functions - Cs.ioc.ee
Binomial Coefficients and Generating Functions - Cs.ioc.ee
Binomial Coefficients and Generating Functions - Cs.ioc.ee
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Operations on <strong>Generating</strong> <strong>Functions</strong> (2)<br />
2. Addition<br />
If 〈f0,f1,f2,...〉 ←→ F (x) <strong>and</strong> 〈g0,g1,g2,...〉 ←→ G(x), then<br />
Proof.<br />
〈f0 + g0,f1 + g1,f2 + g2,...〉 ←→ F (x) + G(x).<br />
〈f0 + g0, f1 + g1, f2 + g2, ...〉 ←→<br />
=<br />
∞<br />
∑<br />
n=0<br />
<br />
∞<br />
∑ fnx<br />
n=0<br />
n<br />
<br />
∞<br />
+ ∑ gnx<br />
n=0<br />
n<br />
<br />
= F (x) + G(x)<br />
(fn + gn)x n =<br />
=<br />
Q.E.D.
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