My question reads: Does this formula has mathematical meaning at first place? Is it summable? $$\sum^{\infty}_{k=0}{n\choose k}{m\choose k} x^k$$
Binomial series with two binomial coefficents
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combinatorics
summation
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0Your "infinite" sum is nothing else than a polynomial in $\,x\,$ of degree $\,\max(n,m)\,$ – 2012-10-11