DLMF:8.8.E13 (Q2545)

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DLMF:8.8.E13
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    Statements

    Defining formula
    d d z ⁡ γ ⁡ ( a , z ) = - d d z ⁡ Γ ⁡ ( a , z ) = z a - 1 ⁢ e - z , derivative 𝑧 incomplete-gamma 𝑎 𝑧 derivative 𝑧 incomplete-Gamma 𝑎 𝑧 superscript 𝑧 𝑎 1 superscript 𝑒 𝑧 {\displaystyle{\displaystyle\frac{\mathrm{d}}{\mathrm{d}z}\gamma\left(a,z% \right)=-\frac{\mathrm{d}}{\mathrm{d}z}\Gamma\left(a,z\right)=z^{a-1}e^{-z},}}
    0 references
    DLMF id
    DLMF:8.8.E13
    0 references
    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.m2adec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2akdec
    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.m2acdec
    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.E1.m2acdec
    0 references
    Q11323
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C8.S1.XMD2.m1ldec
    0 references
    Q11324
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C8.S1.XMD3.m1ldec
    0 references
     
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