  The moments of the single inclusive momentum distribution of hadrons in QCD
jets, are studied in the next-to-modified-leading-log approximation (NMLLA)
including next-to-leading-order (NLO) corrections to the alpha_s strong
coupling. The evolution equations are solved using a distorted Gaussian
parametrisation, which successfully reproduces the spectrum of charged hadrons
of jets measured in e+e- collisions. The energy dependencies of the maximum
peak, multiplicity, width, kurtosis and skewness of the jet hadron distribution
are computed analytically. Comparisons of all the existing jet data measured in
e+e- collisions in the range sqrt(s)~2-200 GeV to the NMLLA+NLO* predictions
allow one to extract a value of the QCD parameter Lambda_QCD, and associated
two-loop coupling constant at the Z resonance alpha_s(m_Z^2)= 0.1195 +/-
0.0022, in excellent numerical agreement with the current world average
obtained using other methods.
