DLMF:2.6.E14 (Q839)

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DLMF:2.6.E14
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    Statements

    Defining formula
    ⟨ t - s - 1 , ϕ ⟩ = - 1 s ! ⁢ ∫ 0 ∞ ( ln ⁡ t ) ⁢ ϕ ( s + 1 ) ⁢ ( t ) ⁢ d t , distribution superscript 𝑡 𝑠 1 italic-ϕ 1 𝑠 superscript subscript 0 𝑡 superscript italic-ϕ 𝑠 1 𝑡 𝑡 {\displaystyle{\displaystyle\left\langle t^{-s-1},\phi\right\rangle=-\frac{1}{% s!}\int_{0}^{\infty}(\ln t)\phi^{(s+1)}(t)\mathrm{d}t,}}
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    DLMF id
    DLMF:2.6.E14
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    constraint
    ϕ ∈ 𝒯 italic-ϕ 𝒯 {\displaystyle{\displaystyle\phi\in\mathcal{T}}}
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