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Category: Integration

let-give-B-x-y-0-1-u-x-1-1-u-y-1-du-and-beta-function-and-x-0-u-x-1-e-u-du-x-gt-0-gamma-function-of-euler-1-prove-that-x-2-0-u-2x-1-e-u-2-du

Question Number 28442 by abdo imad last updated on 25/Jan/18 letgiveB(x,y)=01ux1(1u)y1duand(betafunction)andΓ(x)=0ux1eudu(x>0)(gammafunctionofeuler)$$\left.\mathrm{1}\right)\:{prove}\:{that}\:\:\:\:\Gamma\left({x}\right)=\:\mathrm{2}\int_{\mathrm{0}} ^{\infty} \:{u}^{\mathrm{2}{x}−\mathrm{1}}…