let-give-u-n-npi-n-1-pi-e-t-sint-t-with-gt-0-calculate-n-0-u-n-

Question Number 28676 by abdo imad last updated on 28/Jan/18

l e t g i v e u_{n} = \int_{n π}^{(n + 1) π} e^{- λ t} \frac{s i n t}{\sqrt{t}} w i t h λ > 0

c a l c u l a t e \sum_{n = 0}^{+ \infty} u_{n} .

Commented by abdo imad last updated on 30/Jan/18

\sum_{n = 0}^{+ \infty} u_{n} = \int_{0}^{\infty} e^{- λ t} \frac{s i n t}{\sqrt{t}} d t = \sqrt{π} s i n (\frac{π}{4} - \frac{a r c t a n λ}{2}) f r o m

Q 28756 .