  In this paper, we present a more detailed version of our previous work for
three-particle correlations in quark and gluon jets [1]. We give theoretical
results for this observable in the double logarithmic approximation and the
modified leading logarithmic approximation. In both resummation schemes, we use
the formalism of the generating functional and solve the evolution equations
analytically from the steepest descent evaluation of the one-particle
distribution. In addition, in this paper we include predictions beyond the
limiting spectrum approximation and study this observable near the hump of the
single inclusive distribution. We thus provide a further test of the local
parton hadron duality (LPHD) and make predictions for the LHC. The computation
of higher rank correlators is presented in the double logarithmic approximation
and shown to be rather cumbersome.
