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I need to find a closed form expression for the following:

$$\sum_{n=0}^{\infty}\tfrac{a^n}{(n!)(c-bn)}e^{(c-bn)t} \text{ with } a,b,c<1$$

By closed form expression, I mean a formula that can be evaluated in a finite number of standard operations.

Thanks

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    What count as "standard operations"? And why do you believe one exists?2012-03-12
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    I'm not sure how I'd define standard operations, but an infinite sum wouldn't help my case, so I guess I'm looking for a formula with a finite number of terms. As for why it exists, I believe that based on theorem 3.42 in little Rudin.2012-03-12
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    I don't have my little Rudin handy, but I was not aware that it said anything about expressing sums or integrals in finite terms.2012-03-12

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