Abdullah Altın

Extension of gamma, beta and hypergeometric functions

The main object of this paper is to present generalizations of gamma, beta and hypergeometric functions. Some recurrence relations, transformation formulas, operation formulas and integral representations are obtained for these new generalizations.

On a multivariable extension of the Lagrange–Hermite polynomials

The authors introduce a multivariable extension of the familiar Lagrange–Hermite polynomials, which is motivated by the Chan–Chyan–Srivastava multivariable extension of the classical Lagrange polynomials. Then they derive various families of mixed, multilateral, and multilinear generating functions for these polynomials.

Families of linear generating functions for polynomials in two variables

In the present paper, we derive various families of linear, mixed multilateral and multilinear generating functions for a class of polynomials in two variables. Some further results of the above types are also discussed.

A Kantorovich Type of Szasz Operators Including Brenke-Type Polynomials

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 Korovkins theorem. We also present the order of convergence with the help of a classical approach, the second modulus of continuity, and Peetres -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.

On a multivariable extension of the Humbert polynomials

Abstract In this paper, we present a multivariable extension of the Humbert polynomials, which is motivated by the Chan–Chyan–Srivastava multivariable polynomials, the multivariable extension of the familiar Lagrange–Hermite polynomials and Erkus–Srivastava multivariable polynomials. We derive various families of multilinear and mixed multilateral generating functions for these polynomials. Other miscellaneous properties of these multivariable polynomials are also discussed. Some special cases of the results presented in this study are also indicated.

Miscellaneous properties of some multivariable polynomials

Abstract In this paper, we present various integral representations for the Chan–Chyan–Srivastava, Lagrange–Hermite, Erkus–Srivastava multivariable polynomials and extended Jacobi polynomials. Then, we obtain some partial differential equations for the product of any two of them. We show that the Chan–Chyan–Srivastava multivariable polynomials are not orthogonal. We also discuss other miscellaneous properties of the Chan–Chyan–Srivastava, Lagrange–Hermite and Erkus–Srivastava multivariable polynomials.

A note on a family of two-variable polynomials

The main object of this paper is to construct a two-variable analogue of Jacobi polynomials and to give some properties of these polynomials. We show that these polynomials are orthogonal, then we obtain various recurrence formulas for them. Furthermore, we give some integral representations for these polynomials.

A new family of analytic functions defined by means of Rodrigues type formula

Abstract In this article, a class of analytic functions is investigated and their some properties are established. Several recurrence relations and various classes of bilinear and bilateral generating functions for these analytic functions are also derived. Examples of some members belonging to this family of analytic functions are given and differential equations satisfied by these functions are also obtained.

Some Solutions for an Equation of Order of 4p

We obtain all solutions which depend only on r for a singular partial differential equation of order 4p. Here, the operator includes Laplacian and GASPT (Generalized Axially Symmetric Potential Theory) operator.