DLMF:2.11.E7 (Q1032): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q10931 / rank
 
Normal rank
Property / Symbols used: Q10931 / qualifier
 
Defining formula:

asymptotic-expansion {\displaystyle{\displaystyle\sim}}

\asympexp
Property / Symbols used: Q10931 / qualifier
 
xml-id: C2.S1.SS3.p1.m11acdec

Revision as of 17:39, 1 January 2020

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DLMF:2.11.E7
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    Statements

    E p ( z ) 2 π i e - p π i Γ ( p ) z p - 1 + e - z z s = 0 ( - 1 ) s ( p ) s z s , asymptotic-expansion exponential-integral-En 𝑝 𝑧 2 𝜋 𝑖 superscript 𝑒 𝑝 𝜋 𝑖 Euler-Gamma 𝑝 superscript 𝑧 𝑝 1 superscript 𝑒 𝑧 𝑧 superscript subscript 𝑠 0 superscript 1 𝑠 Pochhammer 𝑝 𝑠 superscript 𝑧 𝑠 {\displaystyle{\displaystyle E_{p}\left(z\right)\sim\frac{2\pi ie^{-p\pi i}}{% \Gamma\left(p\right)}z^{p-1}+\frac{e^{-z}}{z}\sum_{s=0}^{\infty}(-1)^{s}\frac{% {\left(p\right)_{s}}}{z^{s}},}}
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    DLMF:2.11.E7
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    Γ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    C5.S2.E1.m2aadec
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    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    C5.S2.SS3.m1aadec
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    asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    C2.S1.SS3.p1.m11acdec
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