Hello,
Recently I want to evaluate some Integrals with Chebyshev polynomials and Bessel functions. I found the Mathematica
came out with no analytical solutions (The results were the same as I typed in.) Therefore I tried
Integrate[Cos[n*theta]*E^(I*w*W*Cos[theta]), {theta, 0, Pi},
Assumptions -> {Element[{W, theta}, Reals], Element[n, Integers]}]
And it still showed no analytical results. However, there is one Bessel identity, which specifies
$ \int_o^\pi \cos n\theta e^{jwW\cos\theta}d\theta=\pi j^n J_n (wW) $
where $J_n$ is the bessel functions of order $n$
Can Mathematica deal with integration with Bessel identities? Or I made any mistakes.