Related papers: Recurrence relations for powers of q-Fibonacci pol…

We derive a general recurrence relation for squares of Fibonacci-like numbers. Various properties are developed, including double binomial summation identites.

In this paper, we study some properties of the q-Appell polynomials, including the recurrence relations and the q-difference equations which extend some known calssical (q=1) results. We also provide the recurrence relations and the…

We show that Genocchi and Bernoulli numbers are closely related to Fibonacci polynomials and derive some q-analogues.

We give an overview about well-known basic properties of two classes of q-Fibonacci and q-Lucas polynomials and offer a common generalization.

In this note, we obtain some identities for the generalized Fibonacci polynomial by using the Q(x) matrix. These identities including the Cassini identity and Honsberger formula can be applied to some polynomial sequences, such as Fibonacci…

We construct the q-analogue of Euler-Barnes' numbers and polynomials, and investigate their some properties.

In this paper we state some conjectures about q-Fibonacci polynomials which for q=1 reduce to well-known results about Fibonacci numbers and Fibonacci polynomials.

A new $q$-analogue of Appell polynomial sequences and their generalizations are introduced and their main characterizations are proved. As consequences new $q$-analogue of Bernoulli and Euler polynomials and numbers is introduced, their…

In this paper we give some relation involving values of q-Bernoulli, q-Euler and Bernstein polynomials. From these relations, we obtain some interesting identities on the q-Bernoulli, q-Euler and Bernstein polynomials.

In this paper we construct $q$-Genocchi numbers and polynomials. By using these numbers and polynomials, we investigate the $q$-analogue of alternating sums of powers of consecutive integers due to Euler.

In this short note, we establish some identities containing sums of binomials with coefficients satisfying third order linear recursive relations. As a result and in particular, we obtain general forms of earlier identities involving…

For the Lucas sequence $\{U_{k}(P,Q)\}$ we discuss the identities such as the well-known Fibonacci identities. We also propose a method for obtaining identities involving recurrence sequences. With the help of which we find an interpolating…

We prove certain identities involving Euler and Bernoulli polynomials that can be treated as recurrences. We use these and also other known identities to indicate connection of Euler and Bernoulli numbers with entries of inverses of certain…

In this paper we construct the q-analogue of Barnes' Bernoulli numbers and plynomials of degree 2, which is an answer to a part of Schlosser's question. Finally, we treat the q-analogue of the sums of powers of consecutive integrs.

In this research, as the new results of our previously proposed definition for the new class of $2D$ $q$-Appell polynomials, we derive some interesting relations including the recurrence relation and partial $q$-difference equation of the…

Starting with some determinants of binomial coefficients which are related to Fibonacci and Lucas polynomials we study similar determinants for some generalizations of these polynomials and their q-analogues.

We introduce new recurrences for the type B and type D Eulerian polynomials, and interpret them combinatorially. These recurrences are analogous to a well-known recurrence for the type A Eulerian polynomials. We also discuss their…

Based on well-known properties of Fibonacci and Lucas numbers and polynomials we give a self-contained approach to some bivariate analogs.

By investigating a recurrence relation about functions, we first give alternative proofs of various identities on Fibonacci numbers and Lucas numbers, and then, make certain well known identities visible via certain trivalent graph…

In this paper we construct the $q$-analogue of Barnes's Bernoulli numbers and polynomials of degree 2, for positive even integers, which is an answer to a part of Schlosser's question. For positive odd integers, Schlosser's question is…