DLMF:2.6.E43 (Q869)

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DLMF:2.6.E43
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    Statements

    test
    t μ - 1 ∗ f = ∑ s = 0 n - 1 a s ⁢ Γ ⁡ ( μ ) ⁢ Γ ⁡ ( 1 - s - α ) Γ ⁡ ( μ + 1 - s - α ) ⁢ t μ - s - α - ∑ s = 1 n c 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 subscript 𝑎 𝑠 Euler-Gamma 𝜇 Euler-Gamma 1 𝑠 𝛼 Euler-Gamma 𝜇 1 𝑠 𝛼 superscript 𝑡 𝜇 𝑠 𝛼 superscript subscript 𝑠 1 𝑛 subscript 𝑐 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}a_{s}\frac{\Gamma% \left(\mu\right)\Gamma\left(1-s-\alpha\right)}{\Gamma\left(\mu+1-s-\alpha% \right)}t^{\mu-s-\alpha}-\sum_{s=1}^{n}c_{s}\frac{\Gamma\left(\mu\right)}{% \Gamma\left(\mu-s+1\right)}t^{\mu-s}+t^{\mu-1}\ast f_{n}}}
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    DLMF id
    DLMF:2.6.E43
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