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

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

Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

\EulerGamma@{\NVar{z}}
Property / Symbols used: gamma function / qualifier
 
xml-id: C5.S2.E1.m2adec

Revision as of 19:34, 1 January 2020

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DLMF:5.8.E1
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    Statements

    Defining formula
    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)},}}
    0 references
    DLMF id
    DLMF:5.8.E1
    0 references
    constraint
    z ≠ 0 , - 1 , - 2 , … 𝑧 0 1 2 … {\displaystyle{\displaystyle z\neq 0,-1,-2,\dots}}
    0 references
    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2adec
    0 references
     
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