DLMF:1.4.E31 (Q110)

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DLMF:1.4.E31
No description defined

    Statements

    Defining formula
    ∫ a b d x n ⁢ ∫ a x n d x n - 1 ⁢ ⋯ ⁢ ∫ a x 2 d x 1 ⁢ ∫ a x 1 f ⁢ ( x ) ⁢ d x = 1 n ! ⁢ ∫ a b ( b - x ) n ⁢ f ⁢ ( x ) ⁢ d x . superscript subscript 𝑎 𝑏 subscript 𝑥 𝑛 superscript subscript 𝑎 subscript 𝑥 𝑛 subscript 𝑥 𝑛 1 ⋯ superscript subscript 𝑎 subscript 𝑥 2 subscript 𝑥 1 superscript subscript 𝑎 subscript 𝑥 1 𝑓 𝑥 𝑥 1 𝑛 superscript subscript 𝑎 𝑏 superscript 𝑏 𝑥 𝑛 𝑓 𝑥 𝑥 {\displaystyle{\displaystyle\int_{a}^{b}\mathrm{d}x_{n}\int_{a}^{x_{n}}\mathrm% {d}x_{n-1}\cdots\int_{a}^{x_{2}}\mathrm{d}x_{1}\int_{a}^{x_{1}}f(x)\mathrm{d}x% =\frac{1}{n!}\int_{a}^{b}(b-x)^{n}f(x)\mathrm{d}x.}}
    0 references
    DLMF id
    DLMF:1.4.E31
    0 references
    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aodec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aadec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aodec
    0 references
    Q10757
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C1.S1.XMD7.m1edec
    0 references
     
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