  Within framework of the quantum calculus, we represent the partition function
and the mass exponent of a multifractal, as well as the average of random
variables distributed over self-similar set, on the basis of the deformed
expansion in powers of the difference $q-1$. For the partition function, such
expansion is shown to be determined by binomial-type combinations of the
Tsallis entropies related to manifold deformations, while the mass exponent
expansion generalizes known relation $\tau_q=D_q(q-1)$. We find the physical
average related to the escort probability in terms of the deformed expansion as
well. It is demonstrated the mass exponent can acquire a singularity that
relates to a phase transition of the multifractal set in the course of its
deformation.
