DLMF:2.6.E35 (Q861)

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DLMF:2.6.E35
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    Statements

    Defining formula
    I μ ⁢ f ⁢ ( x ) = 1 Γ ⁡ ( μ ) ⁢ ( t μ - 1 ∗ f ) ⁢ ( x ) . superscript 𝐼 𝜇 𝑓 𝑥 1 Euler-Gamma 𝜇 ∗ superscript 𝑡 𝜇 1 𝑓 𝑥 {\displaystyle{\displaystyle I^{\mu}f(x)=\frac{1}{\Gamma\left(\mu\right)}(t^{% \mu-1}\ast f)(x).}}
    0 references
    DLMF id
    DLMF:2.6.E35
    0 references
    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2abdec
    0 references
    Q11028
    Defining formula
    μ 𝜇 {\displaystyle{\displaystyle\mu}}
    xml-id
    C2.S6.XMD14.m1adec
    0 references
    fractional integral (locally)
    Defining formula
    I μ superscript 𝐼 𝜇 {\displaystyle{\displaystyle I^{\mu}}}
    xml-id
    C2.S6.XMD15.m1adec
    0 references
    convolution (locally)
    Defining formula
    ∗ ∗ {\displaystyle{\displaystyle\ast}}
    xml-id
    C2.S6.XMD17.m1adec
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