An Identity for Generalized Bernoulli Polynomials

Recognizing the great importance of Bernoulli numbers and Bernoulli polynomials in various branches of mathematics, the present paper develops two results dealing with these objects. The first one proposes an identity for the generalized Bernoulli polynomials, which leads to further generalizations for several relations involving classical Bernoulli numbers and Bernoulli polynomials. In particular, it generalizes a recent identity suggested by Gessel. The second result allows the deduction of similar identities for Fibonacci, Lucas, and Chebyshev polynomials, as well as for generalized Euler polynomials, Genocchi polynomials, and generalized numbers of Stirling

Summation formulae on Reciprocal Sequences

AbstractBy 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 isε-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