DLMF:5.13.E4 (Q2161): Difference between revisions

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Property / constraint
 

ℜ ⁡ ( a + b + c + d ) > 3 𝑎 𝑏 𝑐 𝑑 3 {\displaystyle{\displaystyle\Re(a+b+c+d)>3}}

\realpart@@{(a+b+c+d)}>3
Property / constraint: ℜ ⁡ ( a + b + c + d ) > 3 𝑎 𝑏 𝑐 𝑑 3 {\displaystyle{\displaystyle\Re(a+b+c+d)>3}} / rank
 
Normal rank

Revision as of 16:05, 30 December 2019

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DLMF:5.13.E4
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    Statements

    test
    ∫ - ∞ ∞ d t Γ ⁡ ( a + t ) ⁢ Γ ⁡ ( b + t ) ⁢ Γ ⁡ ( c - t ) ⁢ Γ ⁡ ( d - t ) = Γ ⁡ ( a + b + c + d - 3 ) Γ ⁡ ( a + c - 1 ) ⁢ Γ ⁡ ( a + d - 1 ) ⁢ Γ ⁡ ( b + c - 1 ) ⁢ Γ ⁡ ( b + d - 1 ) , superscript subscript 𝑡 Euler-Gamma 𝑎 𝑡 Euler-Gamma 𝑏 𝑡 Euler-Gamma 𝑐 𝑡 Euler-Gamma 𝑑 𝑡 Euler-Gamma 𝑎 𝑏 𝑐 𝑑 3 Euler-Gamma 𝑎 𝑐 1 Euler-Gamma 𝑎 𝑑 1 Euler-Gamma 𝑏 𝑐 1 Euler-Gamma 𝑏 𝑑 1 {\displaystyle{\displaystyle\int_{-\infty}^{\infty}\frac{\mathrm{d}t}{\Gamma% \left(a+t\right)\Gamma\left(b+t\right)\Gamma\left(c-t\right)\Gamma\left(d-t% \right)}=\frac{\Gamma\left(a+b+c+d-3\right)}{\Gamma\left(a+c-1\right)\Gamma% \left(a+d-1\right)\Gamma\left(b+c-1\right)\Gamma\left(b+d-1\right)},}}
    0 references
    DLMF id
    DLMF:5.13.E4
    0 references
    constraint
    ℜ ⁡ ( a + b + c + d ) > 3 𝑎 𝑏 𝑐 𝑑 3 {\displaystyle{\displaystyle\Re(a+b+c+d)>3}}
    0 references
     
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