Abstract
In this article, the determinantal definition for the Hermite-Sheffer polynomials is established using linear algebra tools. Further, the Hermite-Sheffer matrix polynomials are introduced by means of their generating function.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Appell, P.: Sur Une Classe de Polynômes. Ann. Sci. École. Norm. Sup. 9(2), 119–144 (1880)
Appell, P., Kampé de Fériet, J.: Fonctions Hypergéométriques et Hypersphériques: Polynômes d’ Hermite. Gauthier-Villars, Paris (1926)
Constantine, A.G., Muirhead, R.J.: Partial differential equations for hypergeometic functions of two argument matrix. J. Multivariate Anal. 3, 332–338 (1972)
Costabile, F.A., Longo, E.: A determinantal approach to Appell polynomials. J. Comput. Appl. Math. 234(5), 1528–1542(2010)
Costabile, F.A., Longo, E.: An algebraic approach to Sheffer polynomial sequences. Integral Transforms Spec. Funct. 25(4), 295–311 (2013)
Dattoli, G., Ottaviani, P.L., Torre, A., Vázquez, L.: Evolution operator equations: integration with algebraic and finite difference methods, applications to physical problems in classical and quantum mechanics and quantum field theory. Riv. Nuovo Cimento Soc. Ital. Fis. (4) 20(2), 1–133 (1997)
Jódar, L., Company, R.: Hermite matrix polynomials and second order matrix differential equations. Approx. Theory Appl. (N.S.) 12(2), 20–30 (1996)
Khan, S., Al-Saad, M.W.M., Yasmin, G.: Some properties of Hermite-based Sheffer polynomials. Appl. Math. Comput. 217(5), 2169–2183 (2010)
Khan, S., Raza, N.: 2-variable generalized Hermite matrix polynomials and Lie Algebra representation. Rep. Math. Phys. 66(2), 159–174 (2010)
Roman, S.: The Umbral Calculus. Academic Press, New York (1984)
Schmidlin, D.J.: The bond between causal complex Cepstra and Sheffer polynomials. IEEE Trans. Circuits Syst. II: Express Briefs 52(2), pp. 99–103 (2005)
Acknowledgments
The authors are thankful to the reviewer for useful suggestions toward the improvement of the paper.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer India
About this paper
Cite this paper
Khan, S., Riyasat, M. (2016). Determinantal Approach to Hermite-Sheffer Polynomials. In: Satapathy, S., Raju, K., Mandal, J., Bhateja, V. (eds) Proceedings of the Second International Conference on Computer and Communication Technologies. Advances in Intelligent Systems and Computing, vol 380. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2523-2_51
Download citation
DOI: https://doi.org/10.1007/978-81-322-2523-2_51
Published:
Publisher Name: Springer, New Delhi
Print ISBN: 978-81-322-2522-5
Online ISBN: 978-81-322-2523-2
eBook Packages: EngineeringEngineering (R0)