¿Could somebody tell me how can i write a zero order bessel function in an HermiteGauss basis? Thanks
The HermiteGauss functions (suitably normalized) are orthonormal for an inner product defined by integration, just like $\{\sin(nx),\cos(mx)\}$ as $n,m$ run over positive integers. The coefficients of an expansion of a $J$Bessel function in terms of HermiteGauss functions are computed by integrating the Bessel functions against the various HermiteGauss functions, in a way analogous to how a Fourier expansion is computed. You'll want to be looking at a table of integrals, or maybe Mathematica. (I'm not guaranteeing anything about the convergence of the series; I haven't thought about it that much.) 


Thank you very much! I was thinking in an expansion tabulated yet like those appearing in Gradstein and Ryzhik, but i didn't find it anywhere. 

