DLMF:8.8.E8 (Q2540): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11330 / rank
 
Normal rank
Property / Symbols used: Q11330 / qualifier
 
test:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11330 / qualifier
 
xml-id: C8.S1.XMD5.m1adec

Revision as of 12:48, 2 January 2020

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English
DLMF:8.8.E8
No description defined

    Statements

    test
    γ ⁡ ( a , z ) = Γ ⁡ ( a ) Γ ⁡ ( a - n ) ⁢ γ ⁡ ( a - n , z ) - z a - 1 ⁢ e - z ⁢ ∑ k = 0 n - 1 Γ ⁡ ( a ) Γ ⁡ ( a - k ) ⁢ z - k , incomplete-gamma 𝑎 𝑧 Euler-Gamma 𝑎 Euler-Gamma 𝑎 𝑛 incomplete-gamma 𝑎 𝑛 𝑧 superscript 𝑧 𝑎 1 superscript 𝑒 𝑧 superscript subscript 𝑘 0 𝑛 1 Euler-Gamma 𝑎 Euler-Gamma 𝑎 𝑘 superscript 𝑧 𝑘 {\displaystyle{\displaystyle\gamma\left(a,z\right)=\frac{\Gamma\left(a\right)}% {\Gamma\left(a-n\right)}\gamma\left(a-n,z\right)-z^{a-1}e^{-z}\sum_{k=0}^{n-1}% \frac{\Gamma\left(a\right)}{\Gamma\left(a-k\right)}z^{-k},}}
    0 references
    DLMF id
    DLMF:8.8.E8
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2addec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2afdec
    0 references
    incomplete gamma function
    test
    γ ⁡ ( a , z ) incomplete-gamma 𝑎 𝑧 {\displaystyle{\displaystyle\gamma\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C8.S2.E1.m2abdec
    0 references
    Q11323
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C8.S1.XMD2.m1gdec
    0 references
    Q11324
    test
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C8.S1.XMD3.m1gdec
    0 references
    Q11330
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C8.S1.XMD5.m1adec
    0 references
     
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