DLMF:2.6.E16 (Q841): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11022 / rank
 
Normal rank
Property / Symbols used: Q11022 / qualifier
 
Defining formula:

f n , n ⁢ ( t ) subscript 𝑓 𝑛 𝑛 𝑡 {\displaystyle{\displaystyle f_{n,n}(t)}}

f_{n,n}(t)
Property / Symbols used: Q11022 / qualifier
 
xml-id: C2.S6.XMD7.m1bdec

Latest revision as of 17:11, 1 January 2020

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DLMF:2.6.E16
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    Statements

    Defining formula
    ⟨ f n , ϕ ⟩ = ( - 1 ) n ⁢ ∫ 0 ∞ f n , n ⁢ ( t ) ⁢ ϕ ( n ) ⁢ ( t ) ⁢ d t , distribution subscript 𝑓 𝑛 italic-ϕ superscript 1 𝑛 superscript subscript 0 subscript 𝑓 𝑛 𝑛 𝑡 superscript italic-ϕ 𝑛 𝑡 𝑡 {\displaystyle{\displaystyle\left\langle f_{n},\phi\right\rangle=(-1)^{n}\int_% {0}^{\infty}f_{n,n}(t)\phi^{(n)}(t)\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:2.6.E16
    0 references
    constraint
    ϕ ∈ 𝒯 italic-ϕ 𝒯 {\displaystyle{\displaystyle\phi\in\mathcal{T}}}
    0 references
    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1ajdec
    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.m5addec
    0 references
    Q10784
    Defining formula
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2addec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3ajdec
    0 references
    Q11021
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C2.S6.XMD4.m1bdec
    0 references
    Q11023
    Defining formula
    𝒯 𝒯 {\displaystyle{\displaystyle\mathcal{T}}}
    xml-id
    C2.S6.XMD6.m1ddec
    0 references
    Q11022
    Defining formula
    f n , n ⁢ ( t ) subscript 𝑓 𝑛 𝑛 𝑡 {\displaystyle{\displaystyle f_{n,n}(t)}}
    xml-id
    C2.S6.XMD7.m1bdec
    0 references
     
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