- #1
rainbowed
- 3
- 0
Homework Statement
Let J0(x)=2/[itex]\pi[/itex][itex]\int[/itex]0[itex]\pi[/itex]/2cos(xcos[y])dy. Show that [itex]\int[/itex]0∞J0(x)e-axdx=[itex]\frac{1}{sqrt(1 +a^2)}[/itex].
Homework Equations
Tonelli and Fubini's theorems
The Attempt at a Solution
Basically I'm finding this problem really hard because I've had to teach myself iterated integrals in order to do it, and I'm not sure if I've learned the theory correctly! So far I've tried swapping the integrals (using a combination of Tonelli and Fubini's theorems) which means that I'd have to use integration by parts on e^-ax and cos(xcosy) so that doesn't seem to help... I've also tried not swapping the integrals and using substitution (u=xcosy) but that doesn't make it simpler. Any help would be much appreciated!