DLMF:2.6.E12 (Q837)

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DLMF:2.6.E12
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    Statements

    Defining formula
    ⟨ t - α , ϕ ⟩ = ∫ 0 ∞ t - α ⁢ ϕ ⁢ ( t ) ⁢ d t , distribution superscript 𝑡 𝛼 italic-ϕ superscript subscript 0 superscript 𝑡 𝛼 italic-ϕ 𝑡 𝑡 {\displaystyle{\displaystyle\left\langle t^{-\alpha},\phi\right\rangle=\int_{0% }^{\infty}t^{-\alpha}\phi(t)\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:2.6.E12
    0 references
    constraint
    ϕ ∈ 𝒯 italic-ϕ 𝒯 {\displaystyle{\displaystyle\phi\in\mathcal{T}}}
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    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1afdec
    0 references
    Q10905
    Defining formula
    ⟨ Λ , ϕ ⟩ distribution Λ italic-ϕ {\displaystyle{\displaystyle\left\langle\NVar{\Lambda},\NVar{\phi}\right% \rangle}}
    xml-id
    C1.S16.SS1.p5.m5aadec
    0 references
    Q10784
    Defining formula
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2aadec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3afdec
    0 references
    Q11023
    Defining formula
    𝒯 𝒯 {\displaystyle{\displaystyle\mathcal{T}}}
    xml-id
    C2.S6.XMD6.m1adec
    0 references
     
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