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Results tagged with generating-functions
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user 533922
A generating function is a way of encoding an infinite sequence of numbers by treating them as the coefficients of a formal power series. Tag questions involving generating functions in this.
7
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3
answers
670
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Properties of $P_{n}(x)={e}^{-x}\sum_{k=0}^{\infty}\frac{a_{k,n}{x}^{k}}{k!}$
I know this will sound like a general question, but given the structure $$P_{n}(x)={e}^{-x}\sum_{k=0}^{\infty}\frac{a_{k,n}{x}^{k}}{k!}$$ where $$a_{k,n} = \frac{1}{\prod_{i=1}^{n} (k+2i) }, $$ what a …
0
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Properties of $P_{n}(x)={e}^{-x}\sum_{k=0}^{\infty}\frac{a_{k,n}{x}^{k}}{k!}$
We are going to expand this:
$$({e}^{x})_{n}=\int_{0}^{\nu} \mu \, \cdots \int_{0}^{\gamma} \beta \, \int_{0}^{\beta} \alpha \, \int_{0}^{\alpha} x \ {e}^{x} \,dx\,d\alpha\,d\beta\,d\gamma\cdots\,d\ …