kprokopi
Aug3-04, 11:49 AM
I am trying to calculate (analytically) the integral:
\int_{0}^{\pi} \left [ \frac{ \sin( \frac{k_0 W \cos \theta}{2})}{\cos \theta} \right]^2 J_{0}(k_0 L \sin \theta ) \sin^3 (\theta ) d \theta
where k_0, W, L are constants and J_0 is the Bessel function of the first kind of order zero.
Hint: Maybe we can use sine integrals Si(x)=\int_{0}^{x} \frac{\sin(\tau)}{\tau} d \tau .
Thanks in advance,
kprokopi
\int_{0}^{\pi} \left [ \frac{ \sin( \frac{k_0 W \cos \theta}{2})}{\cos \theta} \right]^2 J_{0}(k_0 L \sin \theta ) \sin^3 (\theta ) d \theta
where k_0, W, L are constants and J_0 is the Bessel function of the first kind of order zero.
Hint: Maybe we can use sine integrals Si(x)=\int_{0}^{x} \frac{\sin(\tau)}{\tau} d \tau .
Thanks in advance,
kprokopi