There exists such an equality which converts the product of Bessel functions of the first and second kind into a Meijer G-funtion, $$x^\mu J_\nu(x)Y_\nu(x)=-\pi^{-1/2}G_{13}^{20}\left(x^2\left| \begin{matrix}(1+\mu)/2\\ \mu/2+\nu, \mu/2,\mu/2-\nu\end{matrix}\right. \right) $$ which is equation (60) in page 220 in book, Higer transcendental functions [1]. However, there was no proof in this book.
Could anyone offer me a proof? A further question is: can we convert $\frac{\sin(t)Y_0(t)}{t}$ into a certain Meijer G-function? Thanks a lot.
[1] Bateman H, Erdelyi A (1953). Higher transcendental functions [M]. McGraw-Hill; New York.