DLMF:2.6.E47 (Q873)

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DLMF:2.6.E47
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    Statements

    Defining formula
    δ n ⁢ ( x ) = ∑ j = 0 n ( n j ) ⁢ Γ ⁡ ( μ + 1 ) Γ ⁡ ( μ + 1 - j ) ⁢ I μ ⁢ ( t n - j ⁢ f n , j ) ⁢ ( x ) , subscript 𝛿 𝑛 𝑥 superscript subscript 𝑗 0 𝑛 binomial 𝑛 𝑗 Euler-Gamma 𝜇 1 Euler-Gamma 𝜇 1 𝑗 superscript 𝐼 𝜇 superscript 𝑡 𝑛 𝑗 subscript 𝑓 𝑛 𝑗 𝑥 {\displaystyle{\displaystyle\delta_{n}(x)=\sum_{j=0}^{n}\genfrac{(}{)}{0.0pt}{% }{n}{j}\frac{\Gamma\left(\mu+1\right)}{\Gamma\left(\mu+1-j\right)}I^{\mu}\left% (t^{n-j}f_{n,j}\right)(x),}}
    0 references
    DLMF id
    DLMF:2.6.E47
    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.m2aidec
    0 references
    Q10754
    Defining formula
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1acdec
    0 references
    Q11028
    Defining formula
    μ 𝜇 {\displaystyle{\displaystyle\mu}}
    xml-id
    C2.S6.XMD14.m1jdec
    0 references
    fractional integral (locally)
    Defining formula
    I μ superscript 𝐼 𝜇 {\displaystyle{\displaystyle I^{\mu}}}
    xml-id
    C2.S6.XMD15.m1ddec
    0 references
    Q11031
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C2.S6.XMD20.m1gdec
    0 references
    Q11036
    Defining formula
    δ n ⁢ ( x ) subscript 𝛿 𝑛 𝑥 {\displaystyle{\displaystyle\delta_{n}(x)}}
    xml-id
    C2.S6.XMD25.m1bdec
    0 references
    Q11022
    Defining formula
    f n , n ⁢ ( t ) subscript 𝑓 𝑛 𝑛 𝑡 {\displaystyle{\displaystyle f_{n,n}(t)}}
    xml-id
    C2.S6.XMD7.m1kdec
    0 references
     
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