$a,b,c,i,m$ are all integers. Does there exist a closed form for $\sum_{p=0}^{i} \binom{a}{p} \binom{b}{i-p} \binom{b+c -(i-p)}{m-i}$?

  • $\begingroup$ CAS says: $\binom{b}{i} \binom{b+c-i}{m-i} \, _3F_2(-a,b+c-i+1,-i;b-i+1,b+c-m+1;1)$ $\endgroup$ Mar 11 '20 at 17:19
  • $\begingroup$ @MariuszIwaniuk, what does the notation $F_2$ stand for? $\endgroup$
    – HerrWarum
    Mar 12 '20 at 4:21
  • $\begingroup$ generalized hypergeometric function $\endgroup$ Mar 12 '20 at 6:04

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