DLMF:3.4.E3 (Q1182)

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DLMF:3.4.E3
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    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 ) ) , subscript superscript 𝑅 𝑛 𝑡 superscript 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),}}
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