DLMF:2.6.E46 (Q872)

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DLMF:2.6.E46
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    Statements

    Defining formula
    I μ ⁢ f ⁢ ( x ) = ∑ s = 0 n - 1 ( - 1 ) s ⁢ a s s ! ⁢ Γ ⁡ ( μ + 1 ) ⁢ d s + 1 d x s + 1 ⁡ ( x μ ⁢ ( ln ⁡ x - γ - ψ ⁡ ( μ + 1 ) ) ) - ∑ s = 1 n d s Γ ⁡ ( μ - s + 1 ) ⁢ x μ - s + 1 x n ⁢ δ n ⁢ ( x ) , superscript 𝐼 𝜇 𝑓 𝑥 superscript subscript 𝑠 0 𝑛 1 superscript 1 𝑠 subscript 𝑎 𝑠 𝑠 Euler-Gamma 𝜇 1 derivative 𝑥 𝑠 1 superscript 𝑥 𝜇 𝑥 digamma 𝜇 1 superscript subscript 𝑠 1 𝑛 subscript 𝑑 𝑠 Euler-Gamma 𝜇 𝑠 1 superscript 𝑥 𝜇 𝑠 1 superscript 𝑥 𝑛 subscript 𝛿 𝑛 𝑥 {\displaystyle{\displaystyle I^{\mu}f(x)=\sum_{s=0}^{n-1}\frac{(-1)^{s}a_{s}}{% s!\Gamma\left(\mu+1\right)}\frac{{\mathrm{d}}^{s+1}}{{\mathrm{d}x}^{s+1}}\left% (x^{\mu}\left(\ln x-\gamma-\psi\left(\mu+1\right)\right)\right)-\sum_{s=1}^{n}% \frac{d_{s}}{\Gamma\left(\mu-s+1\right)}x^{\mu-s}+\frac{1}{x^{n}}\delta_{n}(x)% ,}}
    0 references
    DLMF id
    DLMF:2.6.E46
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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.m2ahdec
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    Euler’s constant
    Defining formula
    γ {\displaystyle{\displaystyle\gamma}}
    xml-id
    C5.S2.E3.m2abdec
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