DLMF:2.6.E39 (Q865)

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DLMF:2.6.E39
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    Statements

    Defining formula
    t μ - 1 ∗ t - s - α = Γ ⁡ ( μ ) ⁢ Γ ⁡ ( 1 - s - α ) Γ ⁡ ( μ + 1 - s - α ) ⁢ t μ - s - α , ∗ superscript 𝑡 𝜇 1 superscript 𝑡 𝑠 𝛼 Euler-Gamma 𝜇 Euler-Gamma 1 𝑠 𝛼 Euler-Gamma 𝜇 1 𝑠 𝛼 superscript 𝑡 𝜇 𝑠 𝛼 {\displaystyle{\displaystyle t^{\mu-1}\ast t^{-s-\alpha}=\frac{\Gamma\left(\mu% \right)\Gamma\left(1-s-\alpha\right)}{\Gamma\left(\mu+1-s-\alpha\right)}t^{\mu% -s-\alpha},}}
    0 references
    DLMF id
    DLMF:2.6.E39
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    constraint
    t > 0 𝑡 0 {\displaystyle{\displaystyle t>0}}
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    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2addec
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    Q11028
    Defining formula
    μ 𝜇 {\displaystyle{\displaystyle\mu}}
    xml-id
    C2.S6.XMD14.m1ddec
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    convolution (locally)
    Defining formula
    ∗ ∗ {\displaystyle{\displaystyle\ast}}
    xml-id
    C2.S6.XMD17.m1edec
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