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I-a-b-0-1-t-a-1-t-b-dt-Note-I-a-b-a-b-1-I-a-1-b-1-show-that-I-a-1-b-I-a-b-1-I-a-b-find-B-a-1-b-1-interms-of-B-a-b-use-I-a-b-I-b-a-and-deduce-I-5-2-3-2-

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Question Number 208908 by alcohol last updated on 26/Jun/24
I(a,b) = ∫_0 ^( 1) t^a (1−t)^b dt Note : I(a,b) = (a/(b+1))I(a−1,b+1) show that • I(a+1, b) + I(a,b+1) = I(a, b) • find B(a+1, b+1) interms of B(a,b) • use I(a,b) = I(b,a) and deduce I((5/2),(3/2))
I(a,b)=∫01ta(1−t)bdtNote:I(a,b)=ab+1I(a−1,b+1)showthat∙I(a+1,b)+I(a,b+1)=I(a,b)∙findB(a+1,b+1)intermsofB(a,b)∙useI(a,b)=I(b,a)anddeduceI(52,32)

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