  We calculate the genuine long-range multi-particle rapidity correlation
functions, $C_{n}(y_1,...,y_n)$ for $n=3,4,5,6$, originating from fluctuations
of the fireball longitudinal shape. In these correlation functions any
contribution from the short-range two-particle correlations, and in general up
to $(n-1)$-particle in $C_n$, is suppressed. The information about the
fluctuating fireball shape in rapidity is encoded in the cumulants of
coefficients of the orthogonal polynomial expansion of particle distributions
in rapidity.
