Polynomial identities involving Pascal's triangle rows
Résumé
In this short report we consider the famous binomial identity
2n=n∑k=0(nk)
Based on it, the following binomial identities are derived
mn=n∑k=0k∑j=0(nk)(kj)(−1)k−jmj,mn=n∑k=0k∑j=0(nj)(n−jk−j)(−1)k−jmj,
where (nk) are binomial coefficients and (m, n) are non-negative integers.
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