Let $q,\ell, M \in \mathbb{N}$ I am not familiar with mathematica, maple or mathlab to, at least see what this sum suppose to be. I am wondering if someone can compute this sum $$ \sum_{m=0}^q\binom{q-m+\ell-1}{q-m}\binom{2m+M-1}{2m} $$


put on hold as off-topic by dkaeae, xskxzr, Evil, vonbrand, David Richerby Aug 14 at 13:17

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  • "This question does not appear to be about computer science, within the scope defined in the help center." – dkaeae, xskxzr, Evil, vonbrand, David Richerby
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  • $\begingroup$ Cross-posted: math.stackexchange.com/q/3320153/5676 $\endgroup$ – Peter Taylor Aug 12 at 6:34
  • $\begingroup$ Check out the book by Petkovsek et all "A = B", it gives algorithms to solve such questions. Be warned, the methods given are not viable for hand computation except for very particular cases (it is typical to have to check hundreds of cases). Most modern computer algebra systems include them, though. $\endgroup$ – vonbrand Aug 12 at 14:10