DLMF:8.19.E15 (Q2701): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: principal branch of logarithm function / rank
 
Normal rank
Property / Symbols used: principal branch of logarithm function / qualifier
 
Defining formula:

ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}

\ln@@{\NVar{z}}
Property / Symbols used: principal branch of logarithm function / qualifier
 
xml-id: C4.S2.E2.m2abdec

Revision as of 14:10, 2 January 2020

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DLMF:8.19.E15
No description defined

    Statements

    Defining formula
    ∂ j ⁡ E p ⁡ ( z ) ∂ ⁡ p j = ( - 1 ) j ⁢ ∫ 1 ∞ ( ln ⁡ t ) j ⁢ t - p ⁢ e - z ⁢ t ⁢ d t , partial-derivative exponential-integral-En 𝑝 𝑧 𝑝 𝑗 superscript 1 𝑗 superscript subscript 1 superscript 𝑡 𝑗 superscript 𝑡 𝑝 superscript 𝑒 𝑧 𝑡 𝑡 {\displaystyle{\displaystyle\frac{{\partial}^{j}E_{p}\left(z\right)}{{\partial p% }^{j}}=(-1)^{j}\int_{1}^{\infty}(\ln t)^{j}t^{-p}e^{-zt}\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:8.19.E15
    0 references
    constraint
    ℜ ⁡ z > 0 𝑧 0 {\displaystyle{\displaystyle\Re z>0}}
    0 references
    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1acdec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aidec
    0 references
    generalized exponential integral
    Defining formula
    E p ⁡ ( z ) exponential-integral-En 𝑝 𝑧 {\displaystyle{\displaystyle E_{\NVar{p}}\left(\NVar{z}\right)}}
    xml-id
    C8.S19.E1.m2asdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3acdec
    0 references
    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2abdec
    0 references
     
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