DLMF:2.6.E39 (Q865): 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.m2addec

Revision as of 17:15, 1 January 2020

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DLMF:2.6.E39
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    Statements

    Defining formula
    t μ - 1 ∗ t - s - α = Γ ⁡ ( μ ) ⁢ Γ ⁡ ( 1 - s - α ) Γ ⁡ ( μ + 1 - s - α ) ⁢ t μ - s - α , ∗ superscript 𝑡 𝜇 1 superscript 𝑡 𝑠 𝛼 Euler-Gamma 𝜇 Euler-Gamma 1 𝑠 𝛼 Euler-Gamma 𝜇 1 𝑠 𝛼 superscript 𝑡 𝜇 𝑠 𝛼 {\displaystyle{\displaystyle t^{\mu-1}\ast t^{-s-\alpha}=\frac{\Gamma\left(\mu% \right)\Gamma\left(1-s-\alpha\right)}{\Gamma\left(\mu+1-s-\alpha\right)}t^{\mu% -s-\alpha},}}
    0 references
    DLMF id
    DLMF:2.6.E39
    0 references
    constraint
    t > 0 𝑡 0 {\displaystyle{\displaystyle t>0}}
    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.m2addec
    0 references
     
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