DLMF:2.6.E48 (Q874)

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DLMF:2.6.E48
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    Statements

    test
    I μ ⁢ f ⁢ ( x ) = 1 Γ ⁡ ( μ ) ⁢ ∫ 0 x ( x - t ) μ - 1 ⁢ t 1 - α ⁢ ( 1 + t ) - 1 ⁢ d t , superscript 𝐼 𝜇 𝑓 𝑥 1 Euler-Gamma 𝜇 superscript subscript 0 𝑥 superscript 𝑥 𝑡 𝜇 1 superscript 𝑡 1 𝛼 superscript 1 𝑡 1 𝑡 {\displaystyle{\displaystyle I^{\mu}f(x)=\frac{1}{\Gamma\left(\mu\right)}\int_% {0}^{x}(x-t)^{\mu-1}t^{1-\alpha}(1+t)^{-1}\mathrm{d}t,}}
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    DLMF id
    DLMF:2.6.E48
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    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2ajdec
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    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aqdec
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    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aqdec
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    Q11028
    test
    μ 𝜇 {\displaystyle{\displaystyle\mu}}
    xml-id
    C2.S6.XMD14.m1kdec
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    fractional integral (locally)
    test
    I μ superscript 𝐼 𝜇 {\displaystyle{\displaystyle I^{\mu}}}
    xml-id
    C2.S6.XMD15.m1edec
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    Q11019
    test
    f ⁢ ( t ) 𝑓 𝑡 {\displaystyle{\displaystyle f(t)}}
    xml-id
    C2.S6.XMD2.m1xdec
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