DLMF:2.3.E4 (Q720)

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DLMF:2.3.E4
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    Statements

    Defining formula
    ∫ a b e i ⁢ x ⁢ t ⁢ q ⁢ ( t ) ⁢ d t ∼ e i ⁢ a ⁢ x ⁢ ∑ s = 0 ∞ q ( s ) ⁢ ( a ) ⁢ ( i x ) s + 1 - e i ⁢ b ⁢ x ⁢ ∑ s = 0 ∞ q ( s ) ⁢ ( b ) ⁢ ( i x ) s + 1 , asymptotic-expansion superscript subscript 𝑎 𝑏 superscript 𝑒 𝑖 𝑥 𝑡 𝑞 𝑡 𝑡 superscript 𝑒 𝑖 𝑎 𝑥 superscript subscript 𝑠 0 superscript 𝑞 𝑠 𝑎 superscript 𝑖 𝑥 𝑠 1 superscript 𝑒 𝑖 𝑏 𝑥 superscript subscript 𝑠 0 superscript 𝑞 𝑠 𝑏 superscript 𝑖 𝑥 𝑠 1 {\displaystyle{\displaystyle\int_{a}^{b}e^{ixt}q(t)\mathrm{d}t\sim e^{iax}\sum% _{s=0}^{\infty}q^{(s)}(a)\left(\frac{i}{x}\right)^{s+1}-e^{ibx}\sum_{s=0}^{% \infty}q^{(s)}(b)\left(\frac{i}{x}\right)^{s+1},}}
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    DLMF id
    DLMF:2.3.E4
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    constraint
    x → + ∞ → 𝑥 {\displaystyle{\displaystyle x\to+\infty}}
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    Symbols used
    Q10931
    Defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11aadec
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