2.3.E19 (Q708)

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2.3.E19
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    Statements

    DLMF defining formula
    I ⁢ ( x ) = ∫ a b e i ⁢ x ⁢ p ⁢ ( t ) ⁢ q ⁢ ( t ) ⁢ d t 𝐼 𝑥 superscript subscript 𝑎 𝑏 superscript 𝑒 𝑖 𝑥 𝑝 𝑡 𝑞 𝑡 𝑡 {\displaystyle{\displaystyle I(x)=\int_{a}^{b}e^{ixp(t)}q(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
    base of natural logarithm
    DLMF defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2ahdec
    0 references
    imaginary unit
    DLMF defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2abdec
    0 references
    integral
    DLMF defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3ajdec
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    real function
    DLMF defining formula
    p ⁢ ( t ) 𝑝 𝑡 {\displaystyle{\displaystyle p(t)}}
    xml-id
    C2.S3.XMD17.m1edec
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    left endpoint
    DLMF defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C2.S3.XMD23.m1dec
    0 references
    right endpoint
    DLMF defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C2.S3.XMD24.m1dec
    0 references
    function (locally)
    DLMF defining formula
    q ⁢ ( t ) 𝑞 𝑡 {\displaystyle{\displaystyle q(t)}}
    xml-id
    C2.S3.XMD6.m1edec
    0 references

    Identifiers

     
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