DLMF:2.6.E17 (Q842)

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DLMF:2.6.E17
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    Statements

    Defining formula
    ⟨ f , ϕ ⟩ = ∑ s = 0 n - 1 a s ⁢ ⟨ t - s - α , ϕ ⟩ - ∑ s = 1 n c s ⁢ ⟨ δ ( s - 1 ) , ϕ ⟩ + ⟨ f n , ϕ ⟩ distribution 𝑓 italic-ϕ superscript subscript 𝑠 0 𝑛 1 subscript 𝑎 𝑠 distribution superscript 𝑡 𝑠 𝛼 italic-ϕ superscript subscript 𝑠 1 𝑛 subscript 𝑐 𝑠 distribution Dirac-delta 𝑠 1 italic-ϕ distribution subscript 𝑓 𝑛 italic-ϕ {\displaystyle{\displaystyle{\left\langle f,\phi\right\rangle}=\sum_{s=0}^{n-1% }a_{s}\left\langle t^{-s-\alpha},\phi\right\rangle-\sum_{s=1}^{n}c_{s}\left% \langle{\delta^{(s-1)}},\phi\right\rangle+\left\langle f_{n},\phi\right\rangle}}
    0 references
    DLMF id
    DLMF:2.6.E17
    0 references
    Symbols used
    Q10915
    Defining formula
    δ ⁡ ( x - a ) Dirac-delta 𝑥 𝑎 {\displaystyle{\displaystyle\delta\left(\NVar{x-a}\right)}}
    xml-id
    C1.S17.SS1.p1.m2adec
    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.m5aedec
    0 references
    Q11024
    Defining formula
    c ≠ 0 𝑐 0 {\displaystyle{\displaystyle c\neq 0}}
    xml-id
    C2.S6.XMD13.m1dec
    0 references
    Q11019
    Defining formula
    f ⁢ ( t ) 𝑓 𝑡 {\displaystyle{\displaystyle f(t)}}
    xml-id
    C2.S6.XMD2.m1ddec
    0 references
    Q11020
    Defining formula
    a n subscript 𝑎 𝑛 {\displaystyle{\displaystyle a_{n}}}
    xml-id
    C2.S6.XMD3.m1bdec
    0 references
    Q11021
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C2.S6.XMD4.m1cdec
    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.m1cdec
    0 references
     
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