An explanation for the similar appearance of two identities involving Dickson polynomials

Identities Involving Two Kinds of q-Euler Polynomials and Numbers

We introduce two kinds of q-Euler polynomials and numbers, and investigate many of their interesting properties. In particular, we establish q-symmetry properties of these q-Euler polynomials, from which we recover the so-called Kaneko-Momiyama identity for the ordinary Euler polynomials, discovered recently by Wu, Sun, and Pan. Indeed, a q-symmetry and q-recurrence formulas among sum of produc...

On Identities Involving Bernoulli and Euler Polynomials

A class of identities satisfied by both Bernoulli and Euler polynomials is established. Recurrence relations for Bernoulli and Euler numbers are derived.

Some identities involving generalized Gegenbauer polynomials

New identities involving Bernoulli and Euler polynomials

Using the finite difference calculus and differentiation, we obtain several new identities for Bernoulli and Euler polynomials; some extend Miki’s and Matiyasevich’s identities, while others generalize a symmetric relation observed by Woodcock and some results due to Sun.

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.