  Since the famous work by Kolmogorov on incompressible turbulence, the
structure-function theory has been a key foundation of modern turbulence study.
Due to the simplicity of Burgers turbulence, structure functions are calculated
to arbitrary orders, which provides numerous implications for other
compressible turbulent systems. We present the derivation of exact
forcing-scale resolving expressions for high-order structure functions of the
burgers turbulence. Compared with the previous theories where the structure
functions are calculated in the inertial range based on the statistics of
shocks, our expressions link high-order structure functions in different orders
without extra information on the flow structure and are valid beyond the
inertial range, therefore they are easily checked by numerical simulations.
