DLMF:2.3.E5 (Q721)

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DLMF:2.3.E5
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    Statements

    Defining formula
    ∫ a ∞ e i ⁢ x ⁢ t ⁢ q ⁢ ( t ) ⁢ d t ∼ e i ⁢ a ⁢ x ⁢ ∑ s = 0 ∞ q ( s ) ⁢ ( a ) ⁢ ( i x ) s + 1 , asymptotic-expansion superscript subscript 𝑎 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 {\displaystyle{\displaystyle\int_{a}^{\infty}e^{ixt}q(t)\mathrm{d}t\sim e^{iax% }\sum_{s=0}^{\infty}q^{(s)}(a)\left(\frac{i}{x}\right)^{s+1},}}
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    DLMF id
    DLMF:2.3.E5
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    constraint
    x → + ∞ → 𝑥 {\displaystyle{\displaystyle x\to+\infty}}
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