The main purpose of this paper is to obtain some properties of orthog- onal matrix polynomials. W... more The main purpose of this paper is to obtain some properties of orthog- onal matrix polynomials. We derive identities for power series satisfied by Laguerre, Hermite and Gegenbauer matrix polynomials. Further- more, for these matrix polynomials, we give raising operators.
In the present paper, we introduce a Stancu type generalization of Sz?sz- Durrmeyer operators inc... more In the present paper, we introduce a Stancu type generalization of Sz?sz- Durrmeyer operators including Brenke type polynomials. We give convergence properties of these operators via Korovkin?s theorem and the order of convergence by using a classical approach. As an example, we consider a Stancu type generalization of the Durrmeyer type integral operators including Hermite polynomials of variance v. Then, we obtain the rates of convergence by using the second modulus of continuity. Also, for these operators including Hermite polynomials of variance v, we present a Voronovskaja type theorem and r-th order generalization of these positive linear operators.
We give a Kantorovich variant of a generalization of Szasz operators defined by means of the Bren... more We give a Kantorovich variant of a generalization of Szasz operators defined by means of the Brenke-type polynomials and obtain convergence properties of these operators by using Korovkin's theorem. We also present the order of convergence with the help of a classical approach, the second modulus of continuity, and Peetre's -functional. Furthermore, an example of Kantorovich type of the operators including Gould-Hopper polynomials is presented and Voronovskaya-type result is given for these operators including Gould-Hopper polynomials.
In the present paper, we consider a class of holomorphic complex functions defined by Rodrigues t... more In the present paper, we consider a class of holomorphic complex functions defined by Rodrigues type formula and we investigate some properties such as generating function and recurrence relations. Also, we discuss some applications of the given results.
Abstract: In the present paper, we derive some families of polynomials. Some further results of t... more Abstract: In the present paper, we derive some families of polynomials. Some further results of these polynomials as generating function, rodrigues formula and recurrence relations are also discussed. Key–Words: Generating function; Rodrigues formula; recurrence relation. 1
The main purpose of this paper is to obtain some properties of orthog- onal matrix polynomials. W... more The main purpose of this paper is to obtain some properties of orthog- onal matrix polynomials. We derive identities for power series satisfied by Laguerre, Hermite and Gegenbauer matrix polynomials. Further- more, for these matrix polynomials, we give raising operators.
Hacettepe Journal of Mathematics and Statistics, 2013
In this paper, we present a generalization (and unification) of a classof Humbert polynomials whi... more In this paper, we present a generalization (and unification) of a classof Humbert polynomials which include well known families of ChanChyan-Srivastava, Lagrange-Hermite and Erkus-Srivastava multivariable polynomials. We derive various families of multilateral and multilinear generating functions for these polynomials. We also obtain othermiscellaneous properties of these polynomials. Furthermore, for somespecial cases of these polynomials, we present hypergeometric representations and give expansions of these polynomials in series of someorthogonal polynomials.
The main object of this paper is to construct a two-variable analogue of extended Jacobi polynomi... more The main object of this paper is to construct a two-variable analogue of extended Jacobi polynomials and to give some properties of these polynomials. We obtain various differential formulae for two-variable extended Jacobi polynomials and give recurrence relations involving these polynomials. We derive various families of bilinear and bilateral generating functions. Furthermore, some special cases of the results are presented in this study.
The main purpose of this paper is to obtain some properties of orthog- onal matrix polynomials. W... more The main purpose of this paper is to obtain some properties of orthog- onal matrix polynomials. We derive identities for power series satisfied by Laguerre, Hermite and Gegenbauer matrix polynomials. Further- more, for these matrix polynomials, we give raising operators.
In the present paper, we introduce a Stancu type generalization of Sz?sz- Durrmeyer operators inc... more In the present paper, we introduce a Stancu type generalization of Sz?sz- Durrmeyer operators including Brenke type polynomials. We give convergence properties of these operators via Korovkin?s theorem and the order of convergence by using a classical approach. As an example, we consider a Stancu type generalization of the Durrmeyer type integral operators including Hermite polynomials of variance v. Then, we obtain the rates of convergence by using the second modulus of continuity. Also, for these operators including Hermite polynomials of variance v, we present a Voronovskaja type theorem and r-th order generalization of these positive linear operators.
We give a Kantorovich variant of a generalization of Szasz operators defined by means of the Bren... more We give a Kantorovich variant of a generalization of Szasz operators defined by means of the Brenke-type polynomials and obtain convergence properties of these operators by using Korovkin's theorem. We also present the order of convergence with the help of a classical approach, the second modulus of continuity, and Peetre's -functional. Furthermore, an example of Kantorovich type of the operators including Gould-Hopper polynomials is presented and Voronovskaya-type result is given for these operators including Gould-Hopper polynomials.
In the present paper, we consider a class of holomorphic complex functions defined by Rodrigues t... more In the present paper, we consider a class of holomorphic complex functions defined by Rodrigues type formula and we investigate some properties such as generating function and recurrence relations. Also, we discuss some applications of the given results.
Abstract: In the present paper, we derive some families of polynomials. Some further results of t... more Abstract: In the present paper, we derive some families of polynomials. Some further results of these polynomials as generating function, rodrigues formula and recurrence relations are also discussed. Key–Words: Generating function; Rodrigues formula; recurrence relation. 1
The main purpose of this paper is to obtain some properties of orthog- onal matrix polynomials. W... more The main purpose of this paper is to obtain some properties of orthog- onal matrix polynomials. We derive identities for power series satisfied by Laguerre, Hermite and Gegenbauer matrix polynomials. Further- more, for these matrix polynomials, we give raising operators.
Hacettepe Journal of Mathematics and Statistics, 2013
In this paper, we present a generalization (and unification) of a classof Humbert polynomials whi... more In this paper, we present a generalization (and unification) of a classof Humbert polynomials which include well known families of ChanChyan-Srivastava, Lagrange-Hermite and Erkus-Srivastava multivariable polynomials. We derive various families of multilateral and multilinear generating functions for these polynomials. We also obtain othermiscellaneous properties of these polynomials. Furthermore, for somespecial cases of these polynomials, we present hypergeometric representations and give expansions of these polynomials in series of someorthogonal polynomials.
The main object of this paper is to construct a two-variable analogue of extended Jacobi polynomi... more The main object of this paper is to construct a two-variable analogue of extended Jacobi polynomials and to give some properties of these polynomials. We obtain various differential formulae for two-variable extended Jacobi polynomials and give recurrence relations involving these polynomials. We derive various families of bilinear and bilateral generating functions. Furthermore, some special cases of the results are presented in this study.
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