I'm about to compute a convolution, which is given as Eq. (12)
Recall the Jacobi expansion of Bessel function, which is given by $\exp(iz\cos\theta)=\sum_mi^mJ_m(z)\exp(im\theta)$, while performing the convolution of two Fourier transforms here we have $$\mathcal{F}\left\{\exp[i(\rho\cos(\Omega t+\phi)+\gamma\cos(2\Omega t+2\phi)]\right\}.$$ I'm just wondering if there's anything related to the Jacobi expansion or some other tricks in performing the convolution here. A Huge thank!