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I would be very grateful for any ideas to find a closed form for the sum:

$$ \sum^\infty_{k=0} \frac{z^k}{\Gamma(1+k) \Gamma(k+m+1)} {}_1F_2\left(1;1+k,m+k;z\right) $$

where $m\in\mathbb{N}$ and $z\in\mathbb{R}^+$.

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A=B by Petkkovsek, Wilf, Zeilberger? –  Martin Rubey May 4 '13 at 14:02
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