Homework Statement
Bessel's equation of order zero can be written
xy''+y'+xy=0
Homework Equations
Denote the solution which is finite a the origin by J[SIZE="1"]0 Show that the Laplace transform of J[SIZE="1"]0 is proportional to (s^2+1)^-1/2
The Attempt at a Solution
To be honest, I just assumed the exp(-|x|) is equal to exp(-x) for x between the minus and positive infinity and did the normal integration. Am I in the right track?
Homework Statement
I have been trying to solve the Fourier transform of exp(-|x|)
Homework Equations
Do I need to split the function into two parts with different limits,i.e. the first has a limit from -infinity to zero and the secod from zero to +infinity. Please advise?
The...