Ghazala Yasmin

Lie-theoretic generating relations of two variable Laguerre polynomials

Abstract Generating relations involving two variable laguerre polynomials L n ( x , y ) are derived. The process involves the construction of a three-dimensional Lie algebra isomorphic to special linear algebra sl (2) with the help of Weisners method by giving suitable interpretations to the index n of the polynomials L n ( x , y ).

Some properties of Hermite-based Sheffer polynomials

Abstract In this paper, the concepts and the formalism associated with monomiality principle and Sheffer sequences are used to introduce family of Hermite-based Sheffer polynomials. Some properties of Hermite–Sheffer polynomials are considered. Further, an operational formalism providing a correspondence between Sheffer and Hermite–Sheffer polynomials is developed. Furthermore, this correspondence is used to derive several new identities and results for members of Hermite–Sheffer family.

Some results involving Hermite-base polynomials and functions using operational methods

This paper is an attempt to stress the usefulness of the operational methods in the theory of special functions. Using operational methods, we derive summation formulae and generating relations involving various forms of Hermite-base polynomials and functions.

Generating Relations of Hermite–Tricomi Functions Using a Representation of Lie Algebra 3

Abstract Motivated by recent studies of the properties of new classes of polynomials constructed in terms of quasi-monomials, certain generating relations involving Hermite–Tricomi functions are obtained. To accomplish this we use the representation 𝑄(𝑤, 𝑚0) of the 3-dimensional Lie algebra 𝑇3. Some special cases are also discussed.

Representation of a Lie Algebra {\cal G}(0,1) and Three Variable Generalized Hermite Polynomials H_{n} (x,y,z)

In this paper, the authors address the problem of framing three variable generalized Hermite polynomials (G.H.P.), H_{n} (x, y, z) , into the context of the representation \uparrow_{\omega, \mu} of a Lie algebra {\cal G}(0,1), thus stressing the mathematical relevance of G.H.P. and representations of Lie algebras. Generating relations involving G.H.P. and associated Laguerre polynomials are obtained following the ideas and methods suggested by Miller.

Certain results for the 2-variable Apostol type and related polynomials

In this article, the 2-variable general polynomials are taken as base with Apostol type polynomials to introduce a family of 2-variable Apostol type polynomials. These polynomials are framed within the context of monomiality principle and their properties are established. Certain summation formulae for these polynomials are also derived. Examples of some members belonging to this family are considered and numbers related to some mixed special polynomials are also explored.

On Generating Relations Involving Generalized Gegenbauer Polynomials

Abstract In this paper, generating relations involving generalized Gegenbauer polynomials are obtained by constructing a three-dimensional Lie algebra isomorphic to special linear algebra sl(2). Further, a number of new interesting relations involving various generalized polynomials are obtained as applications of these generating relations.

Finding symmetry identities for the 2-variable Apostol type polynomials

Abstract The main aim of this article is to established certain symmetry identities for the 2-variable Apostol type polynomials. The symmetry identities for some special polynomials related to the 2-variable Apostol type polynomials are deduced as special cases. Certain interesting examples are considered to establish the symmetry identities for the 2-variable Gould-Hopper-Apostol type, 2-variable generalized Laguerre-Apostol type and 2-variable truncated exponential-Apostol type polynomials. The special cases of the symmetry identities associated with these polynomials are also given.

Some properties of Hermite based Appell matrix polynomials

Abstract In this paper, the Hermite based Appell matrix polynomials are introduced by using certain operational methods. Some properties of these polynomials are considered. Further, some results involving the 2D Appell polynomials are established, which are proved to be useful for the derivation of results involving the Hermite based Appell matrix polynomials.

Some Properties of Generalized Gegenbauer Matrix Polynomials

Various new generalized forms of the Gegenbauer matrix polynomials are introduced using the integral representation method, which allows us to express them in terms of Hermite matrix polynomials. Certain properties for these new generalized Gegenbauer matrix polynomials such as recurrence relations and expansion in terms of Hermite matrix polynomials are derived. Further, several families of bilinear and bilateral generating matrix relations for these polynomials are established and their applications are presented.