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let-x-0-t-x-1-e-t-dt-1-find-x-1-interms-of-x-with-x-gt-0-2-calculate-n-for-n-N-3-calculate-3-2-




Question Number 33896 by math khazana by abdo last updated on 26/Apr/18
let Γ(x)=∫_0 ^∞   t^(x−1)  e^(−t) dt  1) find Γ(x+1) interms of Γ(x)   with x>0  2)calculate Γ(n) for n ∈ N^★   3)calculate Γ((3/2)) .
letΓ(x)=0tx1etdt1)findΓ(x+1)intermsofΓ(x)withx>02)calculateΓ(n)fornN3)calculateΓ(32).
Answered by tanmay.chaudhury50@gmail.com last updated on 27/Apr/18
⌈(3/2)=⌈(1/2+1)  =1/2⌈(1/2)  =1/2(√Π)
(3/2)=(1/2+1)=1/2(1/2)=1/2Π
Answered by tanmay.chaudhury50@gmail.com last updated on 27/Apr/18
1.⌈(x+1)=x.⌈(x)
1.(x+1)=x.(x)
Answered by tanmay.chaudhury50@gmail.com last updated on 27/Apr/18
2.⌈(n)=⌈(n−1+1)               =(n−1)⌈(n−2)               =(n−1)(n−2)⌈(n−3)              thus the value is factorial(n−1)              ⌈(n)=(n−1)!
2.(n)=(n1+1)=(n1)(n2)=(n1)(n2)(n3)thusthevalueisfactorial(n1)(n)=(n1)!

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