DLMF:2.3.E8 (Q724)

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DLMF:2.3.E8
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    Statements

    test
    ∫ 0 ∞ e - x ⁢ t ⁢ q ⁢ ( t ) ⁢ d t ∼ ∑ s = 0 ∞ Γ ⁡ ( s + λ μ ) ⁢ a s x ( s + λ ) / μ , asymptotic-expansion superscript subscript 0 superscript 𝑒 𝑥 𝑡 𝑞 𝑡 𝑡 superscript subscript 𝑠 0 Euler-Gamma 𝑠 𝜆 𝜇 subscript 𝑎 𝑠 superscript 𝑥 𝑠 𝜆 𝜇 {\displaystyle{\displaystyle\int_{0}^{\infty}e^{-xt}q(t)\mathrm{d}t\sim\sum_{s% =0}^{\infty}\Gamma\left(\frac{s+\lambda}{\mu}\right)\frac{a_{s}}{x^{(s+\lambda% )/\mu}},}}
    0 references
    DLMF id
    DLMF:2.3.E8
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    constraint
    x → + ∞ → 𝑥 {\displaystyle{\displaystyle x\to+\infty}}
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    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2adec
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