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I am learning about generating function now, and I am quite confused about where to use EGF and where to use OGF. You know, I could do the exercises following each section, but if there are some mixed exercises, I often don't know whether I should choose OGF or EGF...

In addition, I read this article just now, and I feel also confused about some words in it. Qiaochu said, "In the language of exponential generating functions, differentiation corresponds to a shift in index (this is what we're really going after) and the above($s^n=s\times s^{n-1}$) is equivalent to the identity $\frac{d}{dx} e^{sx}=se^{sx}$." And I don't know how to understand that they are "equivalent".

Thanks in advance.

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    I take it EGF means exponential generating function, OGF means ordinary generating function.2011-11-09
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    You eventually develop a sense of when you should use an OGF, and when you should use an EGF. There's nothing wrong with trying another approach if the first one doesn't pan out, you know.2011-11-09
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    @J. M. Thanks, any ideas for my second para.?2011-11-09
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    Well, if you have $G(x)=a_0+\sum\limits_{k=1}^\infty \frac{a_k x^k}{k!}$, then $G^\prime(x)=\sum\limits_{k=1}^\infty \frac{k a_k x^{k-1}}{k!}=\sum\limits_{k=1}^\infty \frac{a_k x^{k-1}}{(k-1)!}=a_1+\sum\limits_{k=1}^\infty \frac{a_{k+1} x^k}{k!}$...2011-11-09

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