Generalized polynomials and associated operational identities

Some symmetric identities for the generalized Bernoulli, Euler and Genocchi polynomials associated with Hermite polynomials

In 2008, Liu and Wang established various symmetric identities for Bernoulli, Euler and Genocchi polynomials. In this paper, we extend these identities in a unified and generalized form to families of Hermite-Bernoulli, Euler and Genocchi polynomials. The procedure followed is that of generating functions. Some relevant connections of the general theory developed here with the results obtained ...

Some identities involving generalized Gegenbauer polynomials

Generalized Bivariate Fibonacci-Like Polynomials and Some Identities

In [3], H. Belbachir and F. Bencherif generalize to bivariate polynomials of Fibonacci and Lucas, properties obtained for Chebyshev polynomials. They prove that the coordinates of the bivariate polynomials over appropriate basis are families of integers satisfying remarkable recurrence relations. [7], Mario Catalani define generalized bivariate polynomials, from which specifying initial conditi...

Some Identities on the Generalized q-Bernoulli Numbers and Polynomials Associated with q-Volkenborn Integrals

Let p be a fixed prime number. Throughout this paper, Zp, Qp, C, and Cp will, respectively, denote the ring of p-adic rational integer, the field of p-adic rational numbers, the complex number field, and the completion of algebraic closure of Qp. Let N be the set of natural numbers and Z {0} ∪ N. Let νp be the normalized exponential valuation of Cp with |p|p p−νp p p−1. When one talks of q-exte...

Binomial Identities Involving The Generalized Fibonacci Type Polynomials

We present some binomial identities for sums of the bivariate Fi-bonacci polynomials and for weighted sums of the usual Fibonacci polynomials with indices in arithmetic progression.