DLMF:5.8.E1 (Q2085): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10755 / rank
 
Normal rank
Property / Symbols used: Q10755 / qualifier
 
test:

! {\displaystyle{\displaystyle!}}

!
Property / Symbols used: Q10755 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r15.m5adec
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.m1dec
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.m1dec

Latest revision as of 18:34, 1 January 2020

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DLMF:5.8.E1
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    Statements

    Γ ( z ) = lim k k ! k z z ( z + 1 ) ( z + k ) , Euler-Gamma 𝑧 subscript 𝑘 𝑘 superscript 𝑘 𝑧 𝑧 𝑧 1 𝑧 𝑘 {\displaystyle{\displaystyle\Gamma\left(z\right)=\lim_{k\to\infty}\frac{k!k^{z% }}{z(z+1)\cdots(z+k)},}}
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    z 0 , - 1 , - 2 , 𝑧 0 1 2 {\displaystyle{\displaystyle z\neq 0,-1,-2,\dots}}
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    Γ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    C5.S2.E1.m2adec
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    ! {\displaystyle{\displaystyle!}}
    introduction.Sx4.p1.t1.r15.m5adec
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    k 𝑘 {\displaystyle{\displaystyle k}}
    C5.S1.XMD4.m1dec
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    z 𝑧 {\displaystyle{\displaystyle z}}
    C5.S1.XMD7.m1dec
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