The widely known experimental value of the mean coefficient of the inelasticity <K>~0.5 is calculated by the investigation of a connection of the inelasticity with KNO scaling invariant multiplicity distributions of secondary particles.

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It is shown that there is a visible improvement on the fit to the relation between parameters 1/k and m=n/k of the negative binomial describing the multiplicity distribution of secondary charged particles at high energies by using a general solution of the Kolmogorov reverse differential equation for a state branching process.

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