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DLMF:1.9.E71 - MaRDI portal

DLMF:1.9.E71 (Q325)

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DLMF:1.9.E71
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    Statements

    DLMF defining formula
    ∫ a b ∑ n = 0 ∞ f n ⁢ ( t ) ⁢ d t = ∑ n = 0 ∞ ∫ a b f n ⁢ ( t ) ⁢ d t . subscript superscript 𝑏 𝑎 subscript superscript 𝑛 0 subscript 𝑓 𝑛 𝑡 𝑡 subscript superscript 𝑛 0 subscript superscript 𝑏 𝑎 subscript 𝑓 𝑛 𝑡 𝑡 {\displaystyle{\displaystyle\int^{b}_{a}\sum^{\infty}_{n=0}f_{n}(t)\mathrm{d}t% =\sum^{\infty}_{n=0}\int^{b}_{a}f_{n}(t)\mathrm{d}t.}}
    0 references
    Symbols used
    differential of x
    DLMF defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1ajdec
    0 references
    integral
    DLMF defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3ajdec
    0 references
    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C1.S1.XMD7.m1vdec
    0 references

    Identifiers

     
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