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1.15.E47 - MaRDI portal

1.15.E47 (Q559)

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1.15.E47
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    Statements

    DLMF defining formula
    I α ⁢ f ⁢ ( x ) = 1 Γ ⁡ ( α ) ⁢ ∫ 0 x ( x - t ) α - 1 ⁢ f ⁢ ( t ) ⁢ d t . superscript 𝐼 𝛼 𝑓 𝑥 1 Euler-Gamma 𝛼 subscript superscript 𝑥 0 superscript 𝑥 𝑡 𝛼 1 𝑓 𝑡 𝑡 {\displaystyle{\displaystyle I^{\alpha}f(x)=\frac{1}{\Gamma\left(\alpha\right)% }\int^{x}_{0}(x-t)^{\alpha-1}f(t)\mathrm{d}t.}}
    0 references
    Symbols used
    gamma function
    DLMF defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2adec
    0 references
    differential of x
    DLMF defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1audec
    0 references
    integral
    DLMF defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3audec
    0 references

    Identifiers

     
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