We study the classical problem of finding asymptotics for Bessel functions $J_{\nu}(z)$ and $Y_{\nu}(z)$ as argument $z$ order $\nu$ approach infinity. use blow-up analysis to find modulus phase functions; this produces polyhomogeneous conormal joint asymptotic expansions, valid in any regime. As a consequence, our may be differentiated term by with respect either or order, allowing us easily p...