DLMF:2.3.E12 (Q728)

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DLMF:2.3.E12
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    Statements

    test
    ∫ 0 ∞ f ⁢ ( x ⁢ t ) ⁢ q ⁢ ( t ) ⁢ d t ∼ ∑ s = 0 ∞ ℳ ⁡ f ⁡ ( s + λ μ ) ⁢ a s x ( s + λ ) / μ , asymptotic-expansion superscript subscript 0 𝑓 𝑥 𝑡 𝑞 𝑡 𝑡 superscript subscript 𝑠 0 Mellin-transform 𝑓 𝑠 𝜆 𝜇 subscript 𝑎 𝑠 superscript 𝑥 𝑠 𝜆 𝜇 {\displaystyle{\displaystyle\int_{0}^{\infty}f(xt)q(t)\mathrm{d}t\sim\sum_{s=0% }^{\infty}\mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(\frac{s+\lambda}{\mu}% \right)\frac{a_{s}}{x^{(s+\lambda)/\mu}},}}
    0 references
    DLMF id
    DLMF:2.3.E12
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    constraint
    x → + ∞ → 𝑥 {\displaystyle{\displaystyle x\to+\infty}}
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    Symbols used
    Mellin transform
    test
    ℳ ⁡ ( f ) ⁡ ( s ) Mellin-transform 𝑓 𝑠 {\displaystyle{\displaystyle\mathscr{M}\left(\NVar{f}\right)\left(\NVar{s}% \right)}}
    xml-id
    C1.S14.E32.m2adec
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    Q10931
    test
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11afdec
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