Summation formulae on reciprocal sequences

Abstract

By means of series rearrangement, we prove an algebraic identity on the symmetric difference of bivariate Ω -polynomials associated with an arbitrary complex sequence. When the sequence concerned is ε - reciprocal , we find some unusual recurrence relations with binomial polynomials as coefficients. As applications, several interesting summation formulae are established for Bernoulli, Fibonacci, Lucas and Genocchi numbers.