DLMF:2.6.E14 (Q839): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10755 / rank
 
Normal rank
Property / Symbols used: Q10755 / qualifier
 
test:

! {\displaystyle{\displaystyle!}}

!
Property / Symbols used: Q10755 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r15.m5aadec
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
test:

∫ {\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3ahdec
Property / Symbols used
 
Property / Symbols used: principal branch of logarithm function / rank
 
Normal rank
Property / Symbols used: principal branch of logarithm function / qualifier
 
test:

ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}

\ln@@{\NVar{z}}
Property / Symbols used: principal branch of logarithm function / qualifier
 
xml-id: C4.S2.E2.m2adec
Property / Symbols used
 
Property / Symbols used: Q11023 / rank
 
Normal rank
Property / Symbols used: Q11023 / qualifier
 
test:

𝒯 𝒯 {\displaystyle{\displaystyle\mathcal{T}}}

\mathcal{T}
Property / Symbols used: Q11023 / qualifier
 
xml-id: C2.S6.XMD6.m1cdec

Latest revision as of 16:11, 1 January 2020

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English
DLMF:2.6.E14
No description defined

    Statements

    test
    ⟨ 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,}}
    0 references
    DLMF id
    DLMF:2.6.E14
    0 references
    constraint
    ϕ ∈ 𝒯 italic-ϕ 𝒯 {\displaystyle{\displaystyle\phi\in\mathcal{T}}}
    0 references
    Symbols used
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1ahdec
    0 references
    Q10905
    test
    ⟨ Λ , ϕ ⟩ distribution Λ italic-ϕ {\displaystyle{\displaystyle\left\langle\NVar{\Lambda},\NVar{\phi}\right% \rangle}}
    xml-id
    C1.S16.SS1.p5.m5acdec
    0 references
    Q10784
    test
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2acdec
    0 references
    Q10755
    test
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aadec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3ahdec
    0 references
    principal branch of logarithm function
    test
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2adec
    0 references
    Q11023
    test
    𝒯 𝒯 {\displaystyle{\displaystyle\mathcal{T}}}
    xml-id
    C2.S6.XMD6.m1cdec
    0 references
     
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