DLMF:2.6.E4 (Q829): Difference between revisions

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Property / constraint
 

α > 0 𝛼 0 {\displaystyle{\displaystyle\Re\alpha>0}}

\realpart@@{\alpha}>0
Property / constraint: α > 0 𝛼 0 {\displaystyle{\displaystyle\Re\alpha>0}} / rank
 
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Revision as of 15:53, 30 December 2019

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DLMF:2.6.E4
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    0 t α - 1 ( x + t ) α + β d t = Γ ( α ) Γ ( β ) Γ ( α + β ) 1 x β , superscript subscript 0 superscript 𝑡 𝛼 1 superscript 𝑥 𝑡 𝛼 𝛽 𝑡 Euler-Gamma 𝛼 Euler-Gamma 𝛽 Euler-Gamma 𝛼 𝛽 1 superscript 𝑥 𝛽 {\displaystyle{\displaystyle\int_{0}^{\infty}\frac{t^{\alpha-1}}{(x+t)^{\alpha% +\beta}}\mathrm{d}t=\frac{\Gamma\left(\alpha\right)\Gamma\left(\beta\right)}{% \Gamma\left(\alpha+\beta\right)}\frac{1}{x^{\beta}},}}
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    α > 0 𝛼 0 {\displaystyle{\displaystyle\Re\alpha>0}}
    0 references