DLMF:2.6.E44 (Q870)

From testwiki
Revision as of 16:16, 1 January 2020 by imported>Admin (Admin moved page Main Page to Verifying DLMF with Maple and Mathematica)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:2.6.E44
No description defined

    Statements

    test
    t μ - 1 ∗ f = ∑ s = 0 n - 1 ( - 1 ) s ⁢ a s μ ⋅ s ! ⁢ D s + 1 ⁢ ( t μ ⁢ ( ln ⁡ t - γ - ψ ⁡ ( μ + 1 ) ) ) - ∑ s = 1 n d s ⁢ Γ ⁡ ( μ ) Γ ⁡ ( μ - s + 1 ) ⁢ t μ - s + t μ - 1 ∗ f n ∗ superscript 𝑡 𝜇 1 𝑓 superscript subscript 𝑠 0 𝑛 1 superscript 1 𝑠 subscript 𝑎 𝑠 ⋅ 𝜇 𝑠 superscript 𝐷 𝑠 1 superscript 𝑡 𝜇 𝑡 digamma 𝜇 1 superscript subscript 𝑠 1 𝑛 subscript 𝑑 𝑠 Euler-Gamma 𝜇 Euler-Gamma 𝜇 𝑠 1 superscript 𝑡 𝜇 𝑠 ∗ superscript 𝑡 𝜇 1 subscript 𝑓 𝑛 {\displaystyle{\displaystyle t^{\mu-1}\ast f=\sum_{s=0}^{n-1}\frac{(-1)^{s}a_{% s}}{\mu\cdot s!}D^{s+1}\left(t^{\mu}\left(\ln t-\gamma-\psi\left(\mu+1\right)% \right)\right)-\sum_{s=1}^{n}d_{s}\frac{\Gamma\left(\mu\right)}{\Gamma\left(% \mu-s+1\right)}t^{\mu-s}+t^{\mu-1}\ast f_{n}}}
    0 references
    DLMF id
    DLMF:2.6.E44
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2afdec
    0 references
    Euler’s constant
    test
    γ {\displaystyle{\displaystyle\gamma}}
    xml-id
    C5.S2.E3.m2aadec
    0 references
    psi (or digamma) function
    test
    ψ ⁡ ( z ) digamma 𝑧 {\displaystyle{\displaystyle\psi\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E2.m2aadec
    0 references
    Q10755
    test
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5ahdec
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q870&oldid=4864"