let consider ψ(x)=((Γ^′ (x))/(Γ(x))) 1) prove that ∀ a>0 ∫_0 ^1 ψ(a+x)dx=ln(a) 2) prove that ∀ n∈ N^★ ∫


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Question Number 33897 by math khazana by abdo last updated on 26/Apr/18

$l e t c o n s i d e r ψ (x) = \frac{Γ^{^{'}} (x)}{Γ (x)}$ $1) p r o v e t h a t \forall a > 0 \int_{0}^{1} ψ (a + x) d x = l n (a)$ $2) p r o v e t h a t \forall n \in N^{★} \int_{0}^{1} ψ (x) s i n (2 π n x) d x = - \frac{π}{2}$
	Answered by tanmay.chaudhury50@gmail.com last updated on 28/Apr/18

	Answered by tanmay.chaudhury50@gmail.com last updated on 28/Apr/18

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