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Category: Integration

let-B-x-y-0-1-u-x-1-1-u-y-1-du-and-x-0-t-x-1-e-t-dt-1-prove-that-x-2-0-u-2x-1-e-u-2-du-2-give-x-y-at-form-of-double-integrale-3-prove-that-B-x-y-

Question Number 34291 by math khazana by abdo last updated on 03/May/18 $${let}\:{B}\left({x},{y}\right)\:=\:\int_{\mathrm{0}} ^{\mathrm{1}} {u}^{{x}−\mathrm{1}} \left(\mathrm{1}−{u}\right)^{{y}−\mathrm{1}} \:{du}\:\:{and} \\ $$$$\Gamma\left({x}\right)=\:\int_{\mathrm{0}} ^{\infty} \:{t}^{{x}−\mathrm{1}} \:{e}^{−{t}} {dt} \\ $$$$\left.\mathrm{1}\right)\:{prove}\:{that}\:\Gamma\left({x}\right)\:=\:\mathrm{2}\int_{\mathrm{0}}…