DLMF:26.8.E31 (Q7859)

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DLMF:26.8.E31
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    Statements

    Defining formula
    1 k ! ⁢ d k d x k ⁡ f ⁢ ( x ) = ∑ n = k ∞ s ⁡ ( n , k ) n ! ⁢ Δ n f ⁢ ( x ) , 1 𝑘 derivative 𝑥 𝑘 𝑓 𝑥 superscript subscript 𝑛 𝑘 Stirling-number-first-kind-S 𝑛 𝑘 𝑛 superscript forward-difference 𝑛 𝑓 𝑥 {\displaystyle{\displaystyle\frac{1}{k!}\,\frac{{\mathrm{d}}^{k}}{{\mathrm{d}x% }^{k}}f(x)=\sum_{n=k}^{\infty}\frac{s\left(n,k\right)}{n!}\,\Delta^{n}f(x),}}
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    DLMF id
    DLMF:26.8.E31
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