graham higman has defined coset diagrams for psl(2,ℤ). these diagrams are composed of fragments, and the fragments are further composed of two or more circuits. q. mushtaq has proved in 1983 that existence of a certain fragment γ of a coset diagram in a coset diagram is a polynomial f in ℤ[z]. higman has conjectured that, the polynomials related to the fragments are monic and for a fixed degree...

In this paper, we consider an approach based on the elementary matrix theory. other words, take into account generalized Gaussian Fibonacci numbers. context, a general tridiagonal family. Then, obtain determinants of family via Chebyshev polynomials. Moreover, one type matrix, whose are Horadam hybrid polynomials, i.e., most form its by means polynomials second kind. We provided several illustr...

We determine which (ordinary) Riordan arrays are the coefficient arrays of a family of orthogonal polynomials. In so doing, we are led to introduce a family of polynomials, which includes the Boubaker polynomials, and a scaled version of the Chebyshev polynomials, using the techniques of Riordan arrays. We classify these polynomials in terms of the Chebyshev polynomials of the first and second ...

Generalizations of Binet’s theorem are used to produce generalized Pell sequences from two families of silver means. These Pell sequences are also generated from the family of Fibonacci polynomials. A family of Pell-Lucas sequences are also generated from the family of Lucas polynomials and from another generalization of Binet’s formula. A periodic set of cyclic constants are generated from the...

This paper introduces a family of Askey-Wilson type orthogonal polynomials in n variables associated with a root system of type BCn. The family depends, apart from q, on 5 parameters. For n = 1 it specializes to the four-parameter family of one-variable Askey-Wilson polynomials. For any n it contains Macdonald’s two three-parameter families of orthogonal polynomials associated with a root syste...

Limit transitions will be derived between the five parameter family of Askey-Wilson polynomials, the four parameter family of big q-Jacobi polynomials and the three parameter family of little q-Jacobi polynomials in n variables associated with root system BC. These limit transitions generalize the known hierarchy structure between these families in the one variable case. Furthermore it will be ...

The purpose of this work is to analyse a family of mutually orthogonal polynomials on the unit ball with respect to an inner product which includes an additional term on the sphere. First, we will get connection formulas relating classical multivariate orthogonal polynomials on the ball with our family of orthogonal polynomials. Then, using the representation of these polynomials in terms of sp...

In the present note, we introduce a Bezier variant of a new type of Bernstein Durrmeyer operator, which was introduced by Gupta [3]. We estimate the rate of convergence by using the decomposition technique of functions of bounded variation and applying the optimum bound. It is observed that the analysis for our Bezier variant of new Bernstein Durrmeyer operators is different from the usual Bern...