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DLMF:8.8.E15 - MaRDI portal

DLMF:8.8.E15 (Q3245)

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DLMF:8.8.E15
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    Statements

    DLMF 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
    Symbols used
    derivative of $$f$$ with respect to $$x$$
    DLMF 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.m2aadec
    0 references
    incomplete gamma function
    DLMF defining formula
    γ ⁡ ( a , z ) incomplete-gamma 𝑎 𝑧 {\displaystyle{\displaystyle\gamma\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C8.S2.E1.m2addec
    0 references
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C8.S1.XMD2.m1ndec
    0 references
    parameter
    DLMF defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C8.S1.XMD3.m1ndec
    0 references
    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C8.S1.XMD6.m1fdec
    0 references

    Identifiers

     
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