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DLMF:8.8.E14 - MaRDI portal

DLMF:8.8.E14 (Q3244)

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DLMF:8.8.E14
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    Statements

    DLMF defining formula
    ∂ ∂ ⁡ a ⁡ γ * ⁡ ( a , z ) | a = 0 = - E 1 ⁡ ( z ) - ln ⁡ z . evaluated-at partial-derivative 𝑎 incomplete-gamma-star 𝑎 𝑧 𝑎 0 exponential-integral 𝑧 𝑧 {\displaystyle{\displaystyle\left.\frac{\partial}{\partial a}\gamma^{*}\left(a% ,z\right)\right|_{a=0}=-E_{1}\left(z\right)-\ln z.}}
    0 references
    Symbols used
    exponential integral
    DLMF defining formula
    E 1 ⁡ ( z ) exponential-integral 𝑧 {\displaystyle{\displaystyle E_{1}\left(\NVar{z}\right)}}
    xml-id
    C6.S2.E1.m2adec
    0 references
    incomplete gamma function
    DLMF defining formula
    γ * ⁡ ( a , z ) incomplete-gamma-star 𝑎 𝑧 {\displaystyle{\displaystyle\gamma^{*}\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C8.S2.E6.m2aadec
    0 references
    principal branch of logarithm function
    DLMF defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2adec
    0 references
    partial derivative of $$f$$ with respect to $$x$$
    DLMF defining formula
    ∂ ⁡ f ∂ ⁡ x partial-derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}
    xml-id
    C1.S5.E3.m4adec
    0 references
    partial differential of $$x$$
    DLMF defining formula
    ∂ ⁡ x 𝑥 {\displaystyle{\displaystyle\partial\NVar{x}}}
    xml-id
    C1.S5.E3.m2adec
    0 references
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C8.S1.XMD2.m1mdec
    0 references
    parameter
    DLMF defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C8.S1.XMD3.m1mdec
    0 references

    Identifiers

     
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