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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-

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Question Number 34291 by math khazana by abdo last updated on 03/May/18
let B(x,y) = ∫_0 ^1 u^(x−1) (1−u)^(y−1) du and Γ(x)= ∫_0 ^∞ t^(x−1) e^(−t) dt 1) prove that Γ(x) = 2∫_0 ^∞ u^(2x−1) e^(−u^2 ) du 2)give Γ(x)Γ(y) at form of double integrale 3)prove that B(x,y) =((Γ(x)Γ(y))/(Γ(x+y))) 4) calculate B(m,n) for m and n integr naturals
letB(x,y)=∫01ux−1(1−u)y−1duandΓ(x)=∫0∞tx−1e−tdt1)provethatΓ(x)=2∫0∞u2x−1e−u2du2)giveΓ(x)Γ(y)atformofdoubleintegrale3)provethatB(x,y)=Γ(x)Γ(y)Γ(x+y)4)calculateB(m,n)formandnintegrnaturals

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