DLMF:8.8.E16 (Q2548)

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DLMF:8.8.E16
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    Statements

    Defining formula
    d n d z n ⁡ ( z - a ⁢ Γ ⁡ ( a , z ) ) = ( - 1 ) n ⁢ z - a - n ⁢ Γ ⁡ ( a + n , z ) , derivative 𝑧 𝑛 superscript 𝑧 𝑎 incomplete-Gamma 𝑎 𝑧 superscript 1 𝑛 superscript 𝑧 𝑎 𝑛 incomplete-Gamma 𝑎 𝑛 𝑧 {\displaystyle{\displaystyle\frac{{\mathrm{d}}^{n}}{{\mathrm{d}z}^{n}}(z^{-a}% \Gamma\left(a,z\right))=(-1)^{n}z^{-a-n}\Gamma\left(a+n,z\right),}}
    0 references
    DLMF id
    DLMF:8.8.E16
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    Symbols used
    derivative of $$f$$ with respect to $$x$$
    Defining formula
    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    xml-id
    C1.S4.E4.m2abdec
    0 references
    incomplete gamma function
    Defining formula
    Γ ⁡ ( a , z ) incomplete-Gamma 𝑎 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C8.S2.E2.m2addec
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