I have trouble doing this summation:
$$ \sum_{k=0}^{\min(m_1,m_2)} (-1)^k \binom{m_1}{k} \binom{m_2}{k} $$
where $m_1$ and $m_2$ are positive integers.
Can someone help?
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1I remark that the expression equals the coefficient of $x^{m_2}$ in the polynomial $(x+1)^{m_1}(x-1)^{m_2}$, if that helps at all. – Greg Martin Jan 13 '15 at 07:31
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@GregMartin Thank you. – Doris Jan 13 '15 at 07:59
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related: $\sum(-1)^k\binom mk^2$ – Grigory M Jan 13 '15 at 08:15
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@GrigoryM Thank you. I kind of understood how to do it. – Doris Jan 13 '15 at 08:52
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cf. http://math.stackexchange.com/q/858250/ – Grigory M Jan 13 '15 at 10:13