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!