DLMF:2.6.E26 (Q851): 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.m1edec

Latest revision as of 17:13, 1 January 2020

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DLMF:2.6.E26
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    Statements

    Defining formula
    lim ε → 0 ⁡ ⟨ f n , ϕ ε ⟩ = n ! ⁢ ∫ 0 ∞ f n , n ⁢ ( t ) ( t + z ) n + 1 ⁢ d t . subscript → 𝜀 0 distribution subscript 𝑓 𝑛 subscript italic-ϕ 𝜀 𝑛 superscript subscript 0 subscript 𝑓 𝑛 𝑛 𝑡 superscript 𝑡 𝑧 𝑛 1 𝑡 {\displaystyle{\displaystyle\lim_{\varepsilon\to 0}\left\langle f_{n},\phi_{% \varepsilon}\right\rangle=n!\int_{0}^{\infty}\frac{f_{n,n}(t)}{(t+z)^{n+1}}% \mathrm{d}t.}}
    0 references
    DLMF id
    DLMF:2.6.E26
    0 references
    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1akdec
    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.m5akdec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aedec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3akdec
    0 references
    Q11026
    Defining formula
    ε 𝜀 {\displaystyle{\displaystyle\varepsilon}}
    xml-id
    C2.S6.XMD11.m1ddec
    0 references
    Q11021
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C2.S6.XMD4.m1edec
    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.m1edec
    0 references
     
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