DLMF:2.5.E44 (Q820)

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DLMF:2.5.E44
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    Statements

    test
    ℒ ⁡ h ⁡ ( ζ ) ∼ ∑ n = 0 ∞ b n ⁢ Γ ⁡ ( 1 - β n ) ⁢ ζ β n - 1 + ∑ n = 0 ∞ ( - ζ ) n n ! ⁢ ℳ ⁡ h ⁡ ( n + 1 ) , asymptotic-expansion Laplace-transform ℎ 𝜁 superscript subscript 𝑛 0 subscript 𝑏 𝑛 Euler-Gamma 1 subscript 𝛽 𝑛 superscript 𝜁 subscript 𝛽 𝑛 1 superscript subscript 𝑛 0 superscript 𝜁 𝑛 𝑛 Mellin-transform ℎ 𝑛 1 {\displaystyle{\displaystyle\mathscr{L}\mskip-3.0mu h\mskip 3.0mu \left(\zeta% \right)\sim\sum_{n=0}^{\infty}b_{n}\Gamma\left(1-\beta_{n}\right)\zeta^{\beta_% {n}-1}+\sum\limits_{n=0}^{\infty}\frac{(-\zeta)^{n}}{n!}\mathscr{M}\mskip-3.0% mu h\mskip 3.0mu \left(n+1\right),}}
    0 references
    DLMF id
    DLMF:2.5.E44
    0 references
    constraint
    ζ → 0 + → 𝜁 limit-from 0 {\displaystyle{\displaystyle\zeta\to 0+}}
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2agdec
    0 references
    Laplace transform
    test
    ℒ ⁡ ( f ) ⁡ ( s ) Laplace-transform 𝑓 𝑠 {\displaystyle{\displaystyle\mathscr{L}\left(\NVar{f}\right)\left(\NVar{s}% \right)}}
    xml-id
    C1.S14.E17.m2acdec
    0 references
     
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