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DLMF:8.19.E14 - MaRDI portal

DLMF:8.19.E14 (Q3398)

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DLMF:8.19.E14
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    Statements

    DLMF defining formula
    d d z ⁡ ( e z ⁢ E p ⁡ ( z ) ) = e z ⁢ E p ⁡ ( z ) ⁢ ( 1 + p - 1 z ) - 1 z . derivative 𝑧 superscript 𝑒 𝑧 exponential-integral-En 𝑝 𝑧 superscript 𝑒 𝑧 exponential-integral-En 𝑝 𝑧 1 𝑝 1 𝑧 1 𝑧 {\displaystyle{\displaystyle\frac{\mathrm{d}}{\mathrm{d}z}(e^{z}E_{p}\left(z% \right))=e^{z}E_{p}\left(z\right)\left(1+\frac{p-1}{z}\right)-\frac{1}{z}.}}
    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
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    base of natural logarithm
    DLMF defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2ahdec
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    generalized exponential integral
    DLMF defining formula
    E p ⁡ ( z ) exponential-integral-En 𝑝 𝑧 {\displaystyle{\displaystyle E_{\NVar{p}}\left(\NVar{z}\right)}}
    xml-id
    C8.S19.E1.m2ardec
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    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C8.S1.XMD2.m1ldec
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    parameter
    DLMF defining formula
    p 𝑝 {\displaystyle{\displaystyle p}}
    xml-id
    C8.S1.XMD4.m1jdec
    0 references

    Identifiers

     
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