A note on the post quantum-Sheffer polynomial sequences
-
Subuhi Khan
und
Mehnaz Haneef
Abstract
In this article, the post quantum analogue of Sheffer polynomial sequences is introduced using concepts of post quantum calculus. The series representation, recurrence relations, determinant expression and certain other properties of this class are established. Further, the 2D-post quantum-Sheffer polynomials are introduced via generating function and their properties are established. Certain identities and integral representations for the 2D-post quantum-Hermite polynomials, 2D-post quantum-Laguerre polynomials, and 2D-post quantum-Bessel polynomials are also considered.
Acknowledgements
The detailed remarks mentioned by the reviewer(s) provided great help in overall presentation of the paper. The authors are deeply indebted to the Reviewer(s) for several useful comments and suggestions towards the improvement of the paper.
References
[1] A. Aral, V. Gupta and R. P. Agarwal, Applications of q-Calculus in Operator Theory, Springer, New York, 2013. 10.1007/978-1-4614-6946-9Suche in Google Scholar
[2] F. Costabile, F. Dell’Accio and M. I. Gualtieri, A new approach to Bernoulli polynomials, Rend. Mat. Appl. (7) 26 (2006), no. 1, 1–12. Suche in Google Scholar
[3]
R. Jagannathan,
[4]
R. Jagannathan and R. Sridhar,
[5]
P. Njionou Sadjang,
On the fundamental theorem of
[6]
P. Njionou Sadjang,
On
[7]
P. Njionou Sadjang and U. Duran,
On two bivariate kinds of
[8] E. D. Rainville, Special Functions, The Macmillan, New York, 1960. Suche in Google Scholar
[9] I. M. Sheffer, Some properties of polynomial sets of type zero, Duke Math. J. 5 (1939), 590–622. 10.1215/S0012-7094-39-00549-1Suche in Google Scholar
[10]
F. Soleyman, P. Njionou Sadjang, M. Masjed-Jamei and I. Area,
© 2024 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- The C*-algebra of the Boidol group
- Profinite genus of fundamental groups of compact flat manifolds with the cyclic holonomy group of square-free order
- Positive rigs
- Torus bundles over lens spaces
- Topological amenability of semihypergroups
- On projections of the tails of a power
- Li–Yorke chaos for composition operators on Orlicz spaces
- A note on the post quantum-Sheffer polynomial sequences
- Finite rigid sets of the non-separating curve complex
- Building planar polygon spaces from the projective braid arrangement
- Octonionic monogenic and slice monogenic Hardy and Bergman spaces
- Transcendence on algebraic groups
- An explicit version of Bombieri’s log-free density estimate and Sárközy’s theorem for shifted primes
- The ideal structure of partial skew groupoid rings with applications to topological dynamics and ultragraph algebras
- Joint distribution of the cokernels of random p-adic matrices II
Artikel in diesem Heft
- Frontmatter
- The C*-algebra of the Boidol group
- Profinite genus of fundamental groups of compact flat manifolds with the cyclic holonomy group of square-free order
- Positive rigs
- Torus bundles over lens spaces
- Topological amenability of semihypergroups
- On projections of the tails of a power
- Li–Yorke chaos for composition operators on Orlicz spaces
- A note on the post quantum-Sheffer polynomial sequences
- Finite rigid sets of the non-separating curve complex
- Building planar polygon spaces from the projective braid arrangement
- Octonionic monogenic and slice monogenic Hardy and Bergman spaces
- Transcendence on algebraic groups
- An explicit version of Bombieri’s log-free density estimate and Sárközy’s theorem for shifted primes
- The ideal structure of partial skew groupoid rings with applications to topological dynamics and ultragraph algebras
- Joint distribution of the cokernels of random p-adic matrices II
