DLMF:2.6.E40 (Q866)

From DRMF
Revision as of 17:15, 1 January 2020 by Admin (talk | contribs) (‎Changed an Item: Add constraint)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:2.6.E40
No description defined

    Statements

    Defining formula
    t μ - 1 ∗ t - s - 1 = ( - 1 ) s μ ⋅ s ! ⁢ D s + 1 ⁢ ( t μ ⁢ ( ln ⁡ t - γ - ψ ⁡ ( μ + 1 ) ) ) , ∗ superscript 𝑡 𝜇 1 superscript 𝑡 𝑠 1 superscript 1 𝑠 ⋅ 𝜇 𝑠 superscript 𝐷 𝑠 1 superscript 𝑡 𝜇 𝑡 digamma 𝜇 1 {\displaystyle{\displaystyle t^{\mu-1}\ast t^{-s-1}=\frac{(-1)^{s}}{\mu\cdot s% !}D^{s+1}\left(t^{\mu}\left(\ln t-\gamma-\psi\left(\mu+1\right)\right)\right),}}
    0 references
    DLMF id
    DLMF:2.6.E40
    0 references
    constraint
    t > 0 𝑡 0 {\displaystyle{\displaystyle t>0}}
    0 references
    Symbols used
    Euler’s constant
    Defining formula
    γ {\displaystyle{\displaystyle\gamma}}
    xml-id
    C5.S2.E3.m2adec
    0 references
    psi (or digamma) function
    Defining formula
    ψ ⁡ ( z ) digamma 𝑧 {\displaystyle{\displaystyle\psi\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E2.m2adec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5agdec
    0 references
    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2acdec
    0 references
    Q11028
    Defining formula
    μ 𝜇 {\displaystyle{\displaystyle\mu}}
    xml-id
    C2.S6.XMD14.m1edec
    0 references
    convolution (locally)
    Defining formula
    ∗ ∗ {\displaystyle{\displaystyle\ast}}
    xml-id
    C2.S6.XMD17.m1fdec
    0 references
    Q11030
    Defining formula
    D 𝐷 {\displaystyle{\displaystyle D}}
    xml-id
    C2.S6.XMD19.m1adec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q866&oldid=24817"