Formula:799

Digital Library of Mathematical Functions ID 2.6.E4

${\displaystyle{\displaystyle\int_{0}^{\infty}\frac{t^{\alpha-1}}{(x+t)^{\alpha+\beta}}\mathrm{d}t=\frac{\Gamma\left(\alpha\right)\Gamma\left(\beta\right)}{\Gamma\left(\alpha+\beta\right)}\frac{1}{x^{\beta}},}}$

Constraint(s)

${\displaystyle{\displaystyle\Re\alpha>0}}$
${\displaystyle{\displaystyle\Re\beta>0}}$

Symbols List

• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\Re}}$: real part
 

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