  In the work we have considered p-adic functional series with binomial
coefficients and discussed its p-adic convergence. Then we have derived a
recurrence relation following with a summation formula which is invariant for
rational argument. More precisely, we have investigated a sufficient condition
under which the p-adic power series converges to a rational invariant sum 0.
Finally we have shown application of the invariant summation formula to get
some intersting relations involving Bernoulli numbers and Bernoulli
polynomials.
