DLMF:8.7.E1 (Q2527): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
test:

e {\displaystyle{\displaystyle\mathrm{e}}}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2adec

Revision as of 12:45, 2 January 2020

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DLMF:8.7.E1
No description defined

    Statements

    test
    γ * ⁡ ( a , z ) = e - z ⁢ ∑ k = 0 ∞ z k Γ ⁡ ( a + k + 1 ) = 1 Γ ⁡ ( a ) ⁢ ∑ k = 0 ∞ ( - z ) k k ! ⁢ ( a + k ) . incomplete-gamma-star 𝑎 𝑧 superscript 𝑒 𝑧 superscript subscript 𝑘 0 superscript 𝑧 𝑘 Euler-Gamma 𝑎 𝑘 1 1 Euler-Gamma 𝑎 superscript subscript 𝑘 0 superscript 𝑧 𝑘 𝑘 𝑎 𝑘 {\displaystyle{\displaystyle\gamma^{*}\left(a,z\right)=e^{-z}\sum_{k=0}^{% \infty}\frac{z^{k}}{\Gamma\left(a+k+1\right)}=\frac{1}{\Gamma\left(a\right)}% \sum_{k=0}^{\infty}\frac{(-z)^{k}}{k!(a+k)}.}}
    0 references
    DLMF id
    DLMF:8.7.E1
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2adec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    0 references
     
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