A new family of two-variable polynomials based on hermite polynomials
-
Esra Erkuş-Duman
and
Hakan Ciftci
Abstract
The aim of this paper is to introduce a new two-variable polynomials defined via Hermite polynomials. In order to construct some fundamental properties of these polynomials, we first derive a generating function relation. By using definition and this generating relation, we arrive at several recurrence relations, an integral representation, some implicit summation formulae, a symmetry identity for these new two-variable polynomials. Furthermore, we obtain some results which give various classes of multilinear and multilateral generating functions. Then, some special cases are presented. Finally, we also give a general class of these new polynomials and prove explicit closed-form formulae of them.
Acknowledgement
The authors would like to thank two anonymous reviewers for providing insightful comments and reading the manuscript carefully.
References
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Articles in the same Issue
- Regular Papers
- Variants of Booleanness: Congruences of a partial frame versus those of its free frame
- Models, coproducts and exchangeability: Notes on states on Baire functions
- Inverse tangent series involving pell and pell-lucas polynomials
- A new family of two-variable polynomials based on hermite polynomials
- Decreasing property and complete monotonicity of two functions constituted via three derivatives of a function involving trigamma function
- On the solvability of a fourth-order differential evolution equation on singular cylindrical domain in R4
- Investigation of an implicit Hadamard fractional differential equation with Riemann-Stieltjes integral boundary condition
- Stability criteria for systems of two first-order linear ordinary differential equations
- A perturbed eigenvalue problem in exterior domain
- On extensions of bilinear maps
- Refinement of seminorm and numerical radius inequalities of semi-Hilbertian space operators
- Weighted composition operators from the Besov space into nth weighted type spaces
- Fuzzy ideal topological vector spaces
- Partial actions on convergence spaces
- On quasi-small loop groups
- Topologies generated by symmetric porosity on normed spaces
- The Alpha Power Rayleigh-G family of distributions
- An alternative for Laplace Birnbaum-Saunders distribution
- Existence of positive solutions for boundary value problems with p-Laplacian operator
