Tagged Questions
2
votes
1answer
42 views
Functional form of a series of a product of Bessels
This question arises from my answer to an inverse Laplace transform question. The result I got took the form
$$ f(t)= e^{-r_0 t/2} H(t-a) \left [ J_0\left(\frac{1}{2} a r_0\right) ...
1
vote
2answers
347 views
Laplace transform of a product of Modified Bessel Functions
Working with a scalar field in 2 dimensions I've come to the following integral, from which I can extract the proper ultraviolet behavior ($a \ll 1$) of the theory:
$\int_0^\infty ...
5
votes
5answers
569 views
How can I evaluate $\int_{-\infty}^{\infty}\frac{e^{-x^2}(2x^2-1)}{1+x^2}dx$?
How can I solve this integral: $$\int_{-\infty}^{\infty}\frac{e^{-x^2}(2x^2-1)}{1+x^2}dx.$$ Can I solve this problem using the Laplace transform? How can I do this?
