DLMF:26.8.E31 (Q7859)

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DLMF:26.8.E31
No description defined

    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),}}
    0 references
    DLMF id
    DLMF:26.8.E31
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    Symbols used
    Q12132
    Defining formula
    s ⁡ ( n , k ) Stirling-number-first-kind-S 𝑛 𝑘 {\displaystyle{\displaystyle s\left(\NVar{n},\NVar{k}\right)}}
    xml-id
    C26.S8.SS1.p1.m5ardec
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    derivative of $$f$$ with respect to $$x$$
    Defining formula
    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    xml-id
    C1.S4.E4.m2adec
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    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aidec
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    Q11097
    Defining formula
    Δ forward-difference {\displaystyle{\displaystyle\Delta}}
    xml-id
    C3.S6.SS1.p1.m2adec
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    Q12173
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C26.S1.XMD1.m1gdec
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    Q12174
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C26.S1.XMD4.m1zdec
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    Q12172
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C26.S1.XMD6.m1aedec
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