Asymptotic behaviour of the Bessel heat kernels

We consider Dirichlet heat kernel $p_a^{(\mu )}(t,x,y)$ for the Bessel differential operator $L^{(\mu )}=\frac{d^2}{d{x}^2}+\frac{2\mu +1}{2x}$, $\mu \in \mathbb{R}$, in half-line $(a,\mathrm{\infty })$, $a>0$, and provide its asymptotic expansions for $xy\mathrm{/}t\to \mathrm{\infty }$.