DLMF:2.6.E13 (Q838)

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DLMF:2.6.E13
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    Statements

    Defining formula
    ⟨ t - s - α , ϕ ⟩ = 1 ( α ) s ⁢ ∫ 0 ∞ t - α ⁢ ϕ ( s ) ⁢ ( t ) ⁢ d t , distribution superscript 𝑡 𝑠 𝛼 italic-ϕ 1 Pochhammer 𝛼 𝑠 superscript subscript 0 superscript 𝑡 𝛼 superscript italic-ϕ 𝑠 𝑡 𝑡 {\displaystyle{\displaystyle\left\langle t^{-s-\alpha},\phi\right\rangle=\frac% {1}{{\left(\alpha\right)_{s}}}\int_{0}^{\infty}t^{-\alpha}\phi^{(s)}(t)\mathrm% {d}t,}}
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    DLMF id
    DLMF:2.6.E13
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    constraint
    ϕ ∈ 𝒯 italic-ϕ 𝒯 {\displaystyle{\displaystyle\phi\in\mathcal{T}}}
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    Symbols used
    Q10759
    Defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1adec
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