Recent content by davyyao

Thanks Ray Vickson and Hallsoflvy for nice answering. I think I make mistake to deal with the unit step function in the integral form. It clear now for me!

Hi~ I recently solve a Laplace transform problem as following L[int{t,0}cosh(t'-1)U(t'-1)dt']=? U(t'-1) is the unit step function(=1 for t'>1, =zero otherwise) According the standard Laplace formula : (1)L[cosh(t-1)U(t-1)]=exp(-s)*s/(s^2-1); (2)L(int{t,0}f(t')dt')=F(s)/s...

Hi , Thanks for mfb and jackmell, I use the residue theorem can obtain final result lim_{n goes to infinity}sqrt(n)*pi*2^(-2n+2) As I see, I guest it goes to zero as n goes to to infinity. However, I numerically plot this integrand and it looks delta-like function. Maybe this integral is...

Hi, I don't know how to calculate the following integral of an even function limit{n goes to ∞} int_{-∞}^{∞}frac{sqrt(n)}{(x^2+1)^n}=? Can this calculus be done by complex integral? I was thinking for a few days and no answer so far : ( Thanks!