  The angular dependence of the cumulative particles production off nuclei near
the kinematical boundary for multistep process is defined by characteristic
polynomials in angular variables $J_N^2(z_N^\theta)$, where $\theta$ is the
polar angle defining the momentum of the final (cumulative) particle,
$z_N^\theta = cos (\theta/N)$, the integer $N$ being the multiplicity of the
process (the number of interactions). Physical argumentation, exploring the
small phase space method, leads to the appearance of equations for these
polynomials $J_N^2[cos(\pi/N)]=0$. The recurrent relations between polynomials
with different $N$ are obtained, and their connection with known in mathematics
Chebyshev polynomials of 2-d kind is established. As a result of this equality,
differential cross section of the cumulative particle production has
characteristic behaviour $d\sigma \sim 1/ \sqrt {\pi - \theta}$ at $\theta \sim
\pi$ (the backward focusing effect). Such behaviour takes place for any
multiplicity of the interaction, beginning with $n=3$, elastic or inelastic
(with resonances excitations in intermediate states), and can be called the
nuclear glory phenomenon, or 'Buddha's light' of cumulative particles.

Nuclear Theory;High Energy Physics - Phenomenology