  On the basis of the deformed series in quantum calculus, we generalize the
partition function and the mass exponent of a multifractal, as well as the
average of a random variable distributed over self-similar set. 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 the known relation $\tau_q=D_q(q-1)$.
We find equation for set of averages related to ordinary, escort, and
generalized probabilities in terms of the deformed expansion as well.
Multifractals related to the Cantor binomial set, exchange currency series, and
porous surface condensates are considered as examples. Keywords:Multifractal
set; Deformation; Power series.
