DLMF:5.8.E2 (Q2086): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11279 / rank
 
Normal rank
Property / Symbols used: Q11279 / qualifier
 
test:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11279 / qualifier
 
xml-id: C5.S1.XMD4.m1adec
Property / Symbols used
 
Property / Symbols used: Q11273 / rank
 
Normal rank
Property / Symbols used: Q11273 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11273 / qualifier
 
xml-id: C5.S1.XMD7.m1adec

Latest revision as of 18:34, 1 January 2020

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DLMF:5.8.E2
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    Statements

    test
    1 Γ ⁡ ( z ) = z ⁢ e γ ⁢ z ⁢ ∏ k = 1 ∞ ( 1 + z k ) ⁢ e - z / k , 1 Euler-Gamma 𝑧 𝑧 superscript 𝑒 𝑧 superscript subscript product 𝑘 1 1 𝑧 𝑘 superscript 𝑒 𝑧 𝑘 {\displaystyle{\displaystyle\frac{1}{\Gamma\left(z\right)}=ze^{\gamma z}\prod_% {k=1}^{\infty}\left(1+\frac{z}{k}\right)e^{-z/k},}}
    0 references
    DLMF id
    DLMF:5.8.E2
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2aadec
    0 references
    Euler’s constant
    test
    γ {\displaystyle{\displaystyle\gamma}}
    xml-id
    C5.S2.E3.m2adec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    0 references
    Q11279
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C5.S1.XMD4.m1adec
    0 references
    Q11273
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C5.S1.XMD7.m1adec
    0 references
     
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