DLMF:3.4.E3 (Q1182)

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DLMF:3.4.E3
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    Statements

    Defining formula
    h ⁢ R n , t ′ = h n + 1 ( n + 1 ) ! ⁢ ( f ( n + 1 ) ⁢ ( ξ 0 ) ⁢ d d t ⁡ ∏ k = n 0 n 1 ( t - k ) + f ( n + 2 ) ⁢ ( ξ 1 ) ⁢ ∏ k = n 0 n 1 ( t - k ) ) , ℎ subscript superscript 𝑅 ′ 𝑛 𝑡 superscript ℎ 𝑛 1 𝑛 1 superscript 𝑓 𝑛 1 subscript 𝜉 0 derivative 𝑡 superscript subscript product 𝑘 subscript 𝑛 0 subscript 𝑛 1 𝑡 𝑘 superscript 𝑓 𝑛 2 subscript 𝜉 1 superscript subscript product 𝑘 subscript 𝑛 0 subscript 𝑛 1 𝑡 𝑘 {\displaystyle{\displaystyle hR^{\prime}_{n,t}=\frac{h^{n+1}}{(n+1)!}\left(f^{% (n+1)}(\xi_{0})\frac{\mathrm{d}}{\mathrm{d}t}\prod_{k=n_{0}}^{n_{1}}(t-k)+f^{(% n+2)}(\xi_{1})\prod_{k=n_{0}}^{n_{1}}(t-k)\right),}}
    0 references
    DLMF id
    DLMF:3.4.E3
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    Symbols used
    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.m2aadec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
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