let-consider-x-x-x-1-prove-that-a-gt-0-0-1-a-x-dx-ln-a-2-prove-that-n-N-0-1-x-sin-2pinx-dx-pi-2-

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