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Signed Stirling numbers of first kind as coefficients
Signed Stirling numbers of the first kind We define the following $$s(n,k) = (1)^{nk} \left[n\atop k\right]$$ Prove the following $$(x)_n = x(x1)(x2)\cdots (xn+1) = \sum_{k=0}^n s(n,k)x^k$$ $$\textit{proof}$$ We already proved that $$x^{(n)} = \sum_{k=0}^n \left[n\atop k\right] x^k$$ Which can be … Continue reading →
Posted in Signed Stirling numbers of first kind, Striling numbers of first kind

Tagged first, formula, generating, kind, proof, Signed, stirling

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