I have encountered a problem during my thesis study. I need to find F(x) in terms of G(y). My statement as follows:
$$\int_{0}^\infty F(x)[x^3*B*J_0(xy)+x^4*J_1(xy)]dx=G(y)$$
where B is a constant, G(y) is an unknown function of (n-1). degree polynomial, and $J_0$ and $J_1$ are the Bessel functions of the first kind. If B was equal to zero, F(x) could be found using Hankel transform as follows:
$$x^3*F(x)=\int_{0}^\infty G(y) *J_1(xy)*y*dy$$
However B is not zero, then How can I represent F(x) in terms of G(y)? Thanks.