On a new class of polynomials

A New Class of q-Fibonacci Polynomials

the simple evaluation (3.2 ). This fact led me to a thorough study of this q-analogue via a combinatorial approach based on Morse code sequences. We show that these q-Fibonacci polynomials satisfy some other recurrences too, generalize some well-known facts for ordinary Fibonacci polynomials to this case, derive their generating function and study the special values Fn(1,−q ) and Fn(1,−1) which...

A new class of generalized Bernoulli polynomials and Euler polynomials

The main purpose of this paper is to introduce and investigate a new class of generalized Bernoulli polynomials and Euler polynomials based on the q-integers. The q-analogues of well-known formulas are derived. The q-analogue of the Srivastava–Pintér addition theorem is obtained. We give new identities involving q-Bernstein polynomials.

A New Class of Orthogonal Polynomials on the Unit Circle

Even though the theory of orthogonal polynomials on the unit circle, also known as the theory of Szegő polynomials, is very extensive, it is less known than the theory of orthogonal polynomials on the real line. One reason for this may be that “beautiful” examples on the theory of Szegő polynomials are scarce. This is in contrast to the wonderful examples of Jacobi, Laguerrer and Hermite polyno...

A New Class of Banach Sequence Spaces

A New Property of a Class of Jacobi Polynomials

Polynomials whose coefficients are successive derivatives of a class of Jacobi polynomials evaluated at x = 1 are stable. This yields a novel and short proof of the known result that the Bessel polynomials are stable polynomials. Stability preserving linear operators are discussed. The paper concludes with three open problems involving the distribution of zeros of polynomials.