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Consider page 6 on section 2 in the following review about renormalons http://arxiv.org/pdf/hep-ph/9807443v2.pdf. Consider the following formal power series

$$R=\sum_{n=0}^\infty{}r_n\alpha^{n+1}$$

where $r_n$ is given by

$$r_n=Ka^n\Gamma(n+1+b).$$

The Borel transform of this formal power series $B[R](t)=\sum_{n=0}^{\infty}r_n\frac{t^n}{n!}$ is claimed in equation (2.8) to be

$$B[R](t)=\frac{K\Gamma(1+b)}{(1-at)^{1+b}}$$

How does this follow?

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